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TABLES 



OF 












BY 



E. SC HUBERT. /^5'/^; J 



COMPUTED FOB THE 



AMERICAN EPHEMERIS AND NAUTICAL ALMANAC, 



UNDER THE SUPERINTENDENCE OF 



COMMANDER CHARLES HENRY DAVIS, U. S. N. 



$nirlt8||()) bs ^ti^u f^ ^l|t S^tattxpi id tjtt llalis. 







+ 



BUREAU OP ORDNANCE AND HYDROGRAPHY, 

WASHINGTON. 

I860. 



^^stJr f^^. 6c} 






J 



kku. A«uJ:.c.c..e Mv^^.^ ®ff'^.. 



CAMBRIDGE: 
ELEOTBOTTPED AND PRINTED BT WELCH, BIOELOW, k. CO., 

UNIVERSITY PRESS. 



REPORT 



TO 



COMMANDER C- H. DAVIS, U. 8. N 



I. ON THE COMPUTATION OF THE GENERAL PERTURBATIONS OF MELPOMENE 

BY JUPITER. 

By ERNEST SCHUBERT. 

FOB the computation of these perturbations, Professor Exckb's method, published in the Berliner Jahrhuch 
for 1857, has been used in order to try it by a complete application to a special case. The basis of the 
work are the following elements : — 

Melpomene. Jupiteb (from Boutard's Tables). 

1854, Jan. 0, Washington Mean Time ; (osculating). 1854, Jan. 0, Washington Mean Time. 

M= 79 56 86.81 o , . iff = 269° 43* 39.1 

, = 15 14 81.52)^ n' = 16 16 53.3 ^ n = 11 58 43.2) ^ 

ft = 150 1 8.21 1 "* P ft' = 19 16 43.7 ^^'^^^^r « = ^« ^^ ^^'^ > 

• = 10 9 4.77 I' = 15 28 17.2) t = 1 18 39.5 

9 = 12 32 46.29 <p = 2 45 55.1 

II = 1019".96852 fi = 299".12861 

loga= 0.3609465 log a = 0.7162370 

The plane of the orbit of Melpomene has been adopted for the fundamental plane, and the major axis for 
the line of the abscissas. The orbit of Jupiter is referred to this fundamental plane by means of the formulas 
on page 390 {Jahrhuch for 1857). 

m! «* 

Now for the computation of — ^- the periphery was divided into 16 parts, so that M and M (the mean 

anomalies of Melpomene and Jupiter) for those 16 points are 0% 22**.5, 45"*, &c. Log m' ** = 5.5760322 in 
units of the seventh decimal-place, and for the Julian year as the unit of time. Each point of the Melpomene 

orbit is combined with all 16 points of the Jupiter orbit, which gives 16 X 16 = 256 values of — ^ . On 

page 354, Professor Encke says that those values can be checked only by double calculation, since it cannot 
be done by the differences in the series obtained for the different M, But I found that, if we arrange the 

quantities —^ according to another principle, they can be tested by differences, which will be shown by the 

following : — 



A. 




B. 




M — 


0^ 


22^.5 


45^ 


67** .5 


90* 


etc 


1419.6 

• 


2117.7 

2110.9 

• 

• 
• 


3722.0 
3515.1 
3583.5 

• 
etc. 


7454.2 
6636.6 
6418.2 
6753.7 

• 

o o 
22.5 & 

45 & 22.5 

67.5 ft 45 

Diff. = 22.5 


11776.2 
11195.8 
10851.5 
11154.1 
12234.1 

• 

• 
• 
• 

o o 
ft 

2SI.5 ft 2SI.5 

45 ft 45 

Diff.= 




11776.2 


9701.8 


5823.7 


3385.1 


2150.3 




7454.2 
3722.0 


11195.8 


M «= 22°.5 
10838.6 


7038.9 


4099.4 




6636.6 


ilf=45° 
10851.5 


12032.8 


8415.1 




2117.7 


3515.1 


Af =67*^.5 
6418.2 


11154.1 


13455.3 






1419.6 


2110.9 


Jf-90^ 
3583.5 


6753.7 


12234.1 








etc. 







ThiB sketch needs no further explanation ; the principle for the arrangement in B from A is very simple, 
and it is ohyious that it is the vertical series in B which can be tested by differences. 

In Table A the values of — ^- are Unctions of M, and they are developed in series of the form, 

"^^ = a^ + rf cosJf -{-y^nM 

+ a" cos 2 JIf + ft" sin 2 J!f . 

It is evident that now in these series the coefficients are functions of M^ and they must be developed in series 
of the same form, that is, for instance, 

a** =;: a* + a' cos iff + /^ sm Jf 

+ a''cos2Jf+/J"8in2iM: 

Each of the latter series must be multiplied with the cos i' M or sin i' M belonging to it, and then, finally, 

by resolving the products of two cosines or sines into sums and differences, we obtain — ^i- developed in series 

of the general form 

a;' cos (» M— i' M) + VI sin (t M— %' M). 

In order to have throughout — f ' M we only have to change the sign of i' and that of the coefficient of 

the sine. 

The formulas for the components of the disturbing force (page 892) are : — 



z, = «'«« 1(1-1) y,} 



Therefore, after having developed —^- according to the above precepts, we subtract from it 



^f- = 2684.3 + 888.2 cos M 

+ 28.1 cos 2 if 
+ 2.0 cos 3 if 
+ 0.1 cos 4 



imd get thus m' x* (-^ — -^). This periodical series is to be multiplied successively with x'^ y\^ and a/j ; 
developed also in periodical series they are : — 



x\ 



--0.37409 + 5.16475 cos if' + 0.25210 sin W 
4- 0.12450 cos 2 iff' -f 0.00608 sin 2 iff 
4- 0.00450 cos 3 Jf' 4- 0.00022 sin 8 if 
4- 0.00019 cos 4 if 



yf^ — +0.02313 — 0.31933 cos iT + 5.14340 sin W 

— 0.00770 cos 2 if 4- 0.12401 sin 2 M' 

— 0.00028 cos 3 if 4- 0.00446 sin 3 W 

4- 0.00019 sin 4 if 

a'l = -^,03518 + 0.49693 cos if + 0.68709 sm W 

4- 0.01336 cos 2 if 4- 0.01657 sin 2 M' 
4- 0.00185 cos 3 if' 4- 0.00060 sin 3 if' 

I- 0.00144 cos 4 M' 
4- 0.00142 cos 5 M' 
4- 0.00142 cos 6 W 
4- 0.00142 cos 7 M' 
4-0.00071 co8 8ir 

After that, the periodical series —55- must be multiplied with — Xi and yi. 



We have 



1 = +0.74808 — 2.25537 cos M 

— 0.24159 cos 2 M 

— 0.03886 cos 3 if 

— 0.00741 cos 4 if 

— 0.00155 cos 5 if 

— 0.00035 cos 6 if 



— yi = 



— 2.22785 sin M 

— 0.23961 sin 2 if 

— 0.03861 sin 3 if 

— 0.00737 sin 4 if 

— 0.00155 sin 5 if 

— 0.00085 sin 6 M 



Finally, after these five multiplications, by forming the sums, we obtain the series for Xi, Yj, Zi. 

wi' «* / 1 1 \ 

I subjoin here now the terms of — q^ and of w' jc* I ^j — -^1 retained for multiplication, the terms smaUer 

than 0.5 having been omitted. 















m'lc* 










■ 
















P" 
















t' 


COS 


sin 


*, «' 


cos 


sin 




i' 


+ 


cos 


sin 


■ 


1' 


cos 


sin 








+4348.2 


0.0 


-4 -1 


- 7.3 


0.0 


6 


-1 


5.6 


- 5.8 


-2 


-2 


- 1.1 


+ 0.5 


1 





-602.6 


+25,8 


-3 -1 


+ 6.3 


- 1.6 


7 


-1 


— 


2.7 


+ 6.6 


-1 


-2 


- 14.0 


- 8.8 


2 





+ 19.8 


-60.9 


-2 -1 


- 6.0 


+ 2.8 


8 


-1 




0.0 


- 3.7 





-2 


+ 195.3 


+ 33.7 


3 





+ 1.3 


- 5.1 


-1 -1 


+ 109.0 


+ 64.1 












1 


-2 


-1174.9 


+156.8 


4 







- 1.6 


-1 


-1384.0 


+ 90.2 


-8 


-2 




0.0 


+ 0.5 


2 


-2 


+2618.4 


-301.3 










1 -1 


+5208.0 


-305.3 


-7 


-2 


+ 


0.5 


- 1.1 


3 


-2 


+ 350.1 


- 13.4 


-8 


-1 


0.0 


- 3.7 


2 -1 


+ 185.2 


+ 26.4 


-6 


-2 


— 


0.8 


+ 0.7 


4 


-2 


+ 77.3 


- 27.7 


-7 


-1 


+ 2.9 


+ 6.7 


3 -1 


+ 48.1 


- 43.1 


-6 


-2 


+ 


1.0 


- 0.5 


5 


-2 


+ 16.1 


- 8.6 


-6 


-1 


- 5.2 


- 5.1 


4 -1 


+ 18.5 


- 7.9 


-4 


-2 


-~ 


1.2 


0.0 


6 


-2 


+ 4.7 


- 1.5 


-6 


-1 


+ 6.6 


+ 2.9 


5 -1 


- 4.4 


+ 0.8 


-3 


-2 


+ 


0.9 


+ 0.5 


7 


-2 


0.0 


- 1.7 















m'l^ 














■ 


• 












P" 
















• 


i' 


COS 


sin 


1- 


t' 


cos 


MB 


• 


•' 


cos 


sin 


• 


i' 


cos 


sin 


• 8 


-2 


0.0 


+ 0.5 


-2 


-4 


+ 0.8 


+ 1.1 


6 


-5 


+ 96.3 


- 21.5 


-5 


-7 


+ 


5.3 


+ 2.6 










-1 


-4 


- 1.1 


- 1.8 


7 


-5 


+ 38.0 


- 11.8 


-4 


-7 


— 


7.4 


0.0 


-8 


-3 


+ 0.5 


+ 1.2 





-4 


+ 3.0 


+ 3.7 


8 


-5 


+ 4.5 


- 1.2 


-3 


-7 


+ 


6.8 


- 3.0 


-7 


-3 


- 0.9 


- 2.9 


1 


-4 


- 31.4 


- 5.3 










-2 


-7- 


— 


5.3 


+ 5.3 


-6 


-3 


+ 2.0 


+ 2.1 


2 


-4 


+ 158.1 


- 19.3 


-8 


-6 


+ 12.7 


- 1.2 


-1 


-7 


+ 


2.4 


- 6.7 


-6 


-3 


- 2.8 


- 1.2 


3 


-4 


- 447.7 


+120.2 ' 


-7 


-6 


+ 4.4 


- 6.8* 





-7 




0.0 


+ 7.4 


-4 


-3 


+ 2.8 


0.0 


4 


-4- 


+ 506.8 


-117.6 


-6 


S 


+ 2.7 


0.0 


1 


-7 


— 


3.1 


- 6.5 


-3 


-3 


- 2.9 


+ 1.1 


5 


-4 


+ 181.6 


- 30.1 


-5 


-6 


+ 1.2 


- 1.0 


2 


-7 


+ 


4.3 


+ 5.1 


-2 


-3 


+ 1.8 


- 2.4 


6 


-4 


+ 52.8 


- 15.4 


-4 


-6 


- 1.0 


0.0 


3 


-7 


— 


2.3 


- 2.7 


-1 


-3 


0.0 


+ 4.8 


7 


-4 


+ 14.7 


- 4.9 


-3 


-6 


+ 0.9 


0.0 


4 


-7 


— 


6.7 


+ 4.7 





-3 


- 27.6 


- 12.0 


8 


-4 


+ 2.2 


- 1.6 


-2 


-6 


- 1.1 


- 0.8 


5 


-7 


+ 


33.9 


- 11.6 


1 


-3 


+ 202.1 


+ 1.6 










-1 


-6 


0.0 


+ 1.0 


6 


-7 


— 


45.4 


+ 23.5 


2 


-3 


- 778.5 


+153.7 


-8 


-5 


+ 4.5 


- 1.2 





-6 


0.0 


- 1.0 


7 


-7 


+ 


23.5 


- 2.9 


3 


-3 


+1199.2 


-205.2 


-7 


-5 


+ 2.8 


- 4.0 


I 


-6 


- 1.2 


+ 0.8 


8 


-7 


+ 


6.9 


- 10.9 


4 


-3 


+ 282.1 


- 30.9 


-6 


-5 


+ 2.6 


+ 1.5 


2 


-6 


+ 5.7 


0.0 












5 


-3 


+ 73.9 


- 21.2 


-5 


-5 


- 2.5 


- 1.5 


3 


-6 


- 22.5 


+ 4.0 


-8 


-8 


+ 


3.6 


0.0 


6 


-3 


+ 15.1 


- 5.3 


-4 


-5 


+ 2.9 


0.0 


4 


-6 


+ 68.9 


- 20.7 


-7 


-8 


— 


6.9 


- 8.9 


7 


-3 


+ 5.8 


- 4.7 


-3 


-5 


- 2.8 


+ 1.1 


5 


-6 


- 116.8 


+ 48.6 


-6 


-8 


+ 


13.0 


+ 3.8 


8 


-3 


+ 0.5 


+ 1.2 


-2 


-5 


+ 1.9 


- 2.1 


6 


-e 


+ 75.3 


- 25.2 


-5 


-8 


— 


3.6 


- 2.4 










-1 


-5 


- 1.3 


+ 2.8 


7 


-6 


+ 46.2 


- 18.2 


-4 


-8 


+ 


1.9 


0.0 


-8 


-4 


+ 2.2 


- 1.6 





-5 


- 0.8 


- 3.2 


8 


-6 


+ 12.7 


- 1.2 


4 


-8 


+ 


1.9 


0.0 


-7 


-4 


0.0 


+ 0.8 


1 


-5 


+ 5.7 


+ 4.3 










5 


-8 


— 


3.6 


+ 2.4 


-6 


-4 


+ 1.3 


- 1.2 


2 


-5 


- 30.7 


- 1.1 


S 


-7 


+ 6.9 


- 10.9 


6 


-8 


+ 


13.0 


- 3.8 


-5 


-4 


- 1.4 


+ 0.6 


3 


-5 


+ 111.6 


- 23.4 


-7 


-7 


+ 24.3 


+ 8.4 


7 


-8 


— 


6.9 


+ 8.9 


-4 


-4 


+ 1.5 


0.0 


4 


-5 


- 240.3 


+ 80.8 


-6 


-7* 


- 6.4 


- 9.8 


8 


-8 


+ 


3.6 


0.0 


-3 


-4 


- 1.6 


- 0.6 


5 


H) 


+ 204.6 


- 59.9 
































^ 

«.'«'(i,- 


i) 














i\ 


• 

t 


cos 


sin 


«•', 


t 


cos 


sin 


«', 


• 

t. 


cos 


sin 


t', 


■ 

t 


COS 


sin 








+1663.9 


0.0 


6 


-1 


- 1.2 


- 0.8 


-4 


-3 


- 1.6 


- 0.6 


1 


-4 


■+ 


18.5 


+ 7.9 


1 





-1772.6 


- 90.2 


7 


-1 


- 3.1 


+ 6.5 


-3 


-3 


- 2.9 


+ 1.1 


2 


-4 


+ 


77.3 


+ 27.7 


2 





+ 167.2 


- 33.7 










-2 


-3 


+ 0.9 


+ 0.5 


3 


-4 


+ 


282.1 


+ 30.9 


3 





- 29.6 


+ 12.0 


-7 


-2 


- 5.3 


+ 5.3 


-1 


~3 


+ 6.3 


- 1.6 


4 


^ 


+ 


506.8 


+117^ 


4 





+ 2.9 


- 3.7 


-6 


-2 


- 1.1 


- 0.8 





-3 


+ 1.3 


+ 5.1 


5 


-4 


— 


240.3 


- 80.8 


5 





- 0.8 


+ 3.2 


-5 


-2 


+ 1.9 


- 2.1 


1 


-3 


+ 48.1 


+ 43.1 


6 


-4 


+ 


68.9 


+ 20.7 


6 





0.0 


+ 1.0 


-4 


-2 


+ 0.8 


+ 1.1 


2 


-3 


+ 350.1 


+ 13.4 


7 


-4 




6.7 


- 4.7 


7 





0.(f 


- 7.4 


-3 
-2 


-2 
-2 


+ 1.8 
- 1.1 


- 2.4 

+ 0.5 


3 
4 


-3 
-3 


+1199.2 
- 447.7 


+205.2 
-120.2 


8 


-4 


+ 


1.9 


0.0 


-7 


—1 


+ 2.4 


- 6.7 


-1 


-2 


- 6.0 


+ 2.8 


5 


-3 


+ 111.6 


+ 23.4 


-8 


-5 


— 


3.6 


- 2.4 


-6 


—1 


0.0 


+ 1.0 





-2 


+ ;i9.8 


+ 60.9 


6 


-3 


- 22.5 


- 4.0 


-7 


-5 


+ 


5.3 


+ 2.6 


-5 


—1 


- 1.3 


+ 2.8 


1 


-2 


+ 185.2 


- 26.4 


7 


-3 


- 2.3 


+ 2.7 


-6 


-5 


+ 


1.2 


- 1.0 


-4 


—1 


- 1.1 


- 1.8 


2 


-2 


+2618.4 


+301.3 










-5 


-5 


— 


2.5 


- 1.5 


-3 


—J 


0.0 


+ 4.8 


3 


-2 


- 778.5 


-153.7 


-8 


-4 


+ 1.9 


0.0 


-4 


-5 


— 


1.4 


+ 0.6 


-2 


-1 


- 14.0 


- 8.8 


4 


-2 


+ 158.1 


+ 19.3 


-7 


-4 


- 7.4 


0.0 


-3 


-5 


— 


2.8 


- 1.2 


-1 


—1 


+ 109.0 


+ 64.1 


5 


-2 


- 30.7 


+ 1.1 


-6 


-4 


- 1.0 


0.0 


-2 


-5 


+ 


1.0 


- 0.5 





—1 


- 602.6 


- 25.8 


6 


~2 


+ 5.7 


0.0 


-5 


-4 


+ 2.9 


0.0 


-1 


-5 


+ 


6.6 


+ 2.9 


1 


—1 


+5208.0 


+305.3 


7 


-^ 


+ 4.3 


- 5.1 


-4 


-4 


+ 1.5 


e.o 





-5 




0.0 


0.0 


2 


~~1 


-1174.9 


-156.8 










-3 


-4 


+ 2.8 


0.0 


1 


-5 


— 


4.4 


- 0.8 


3 


—1 


+ 202.1 


- 1.6 


-7 


-3 


+ 6.8 


- 3U) 


-2 


-4 


- 1.2 


0.0 


2 


-5 


+ 


16.1 


+ 8.6 


4 


—1 


- 31.4 


+ 5.3 


-6 


-3 


+ 0.9 


0.0 


-1 


-4 


- 7.3 


0.0 


3 


-5 


+ 


73.9 


+ 2142 


5 


—1 


+ 5.7 


- 4.3 


-5 


-^3 


- 2.8 


+ 1.1 





-4 


0.0 


+ 1.6 


4 


-5 


+ 


181.6 


+ 30.1 



y 





"•'"'C-- 


^) 




t', i 


COS 


sin 


t', i 


cos 


sin 


t', 


• 


cos 


sin 




cos 


sin 


5 -5 


+ 204.6 


+ 59.9 


2 -6 


+ 4.7 


+ 1.5 


-1 


-7 


+ 2.9 


+ 6.7 


-6 -8 


+ 4.5 


- 1.2 


6 -5 


- 116.8 


- 48.6 


3 -6 


+ 15.1 


+ 5.3 





-7 


0.0 


0.0 


-4 -^ 


+ 2.2 


- 1.6 


7 -5 


+ 33.9 


+ 11.6 


4 -6 


+ 52.8 


+ 15.4 


1 


-7 


- ia.7 


- 6.6 


-3 -^ 


+ 0.5 


+ 1.2 


8 -5 


~ 3.6 


- 2.4 


5 -6 


+ 96.3 


+ 21.5 


8 


-7 


0.0 


+ 1.7 


-2 -« 




0.0 


+ 0.5 








6 -6 


+ 75.3 


+ 25.2 


3 


-7 


+ 6.8 


+ 4.7 


-1 -8 




0.0 


- 3.7 


-8 -€ 


+ 13.0 


+ 3.8 


7 -6 


- 45.4 


- 23.5 


4 


-7 


+ 14.7 


+ 4.9 


-8 




0.0 


0.0 


-7 -6 


- 6.4 


- 9.8 


8 -6 


+ 13.0 


+ 3.8 


5 


-7 


+ 88.0 


+ 11.8 


1 -8 




0.0 


+ 3.7 


-€ -€ 


+ 2.7 


0.0 


• 






6 


-7 


+ 46.2 


+ 18.2 


2 S 




0.0 


- 0.5 


-5 -6 


+ 2.6 + 1.5 


-8 -7 


- 6.9 


- 8.9 


7 


-7 


+ 23.5 


+ 2.9 


3-8 + 0.6 


- 1.2 


-4 -6 


+ 1.3 - 1.2 


-7 -7 


+ 24.3 


+ 8.4 


8 


-7 


- 6.9 


- 8.9 


4 -8 + 2.2 


+ 1.6 


-3 -6 


+ 2.0 + 2.1 


-6 -7 


+ 4.4 


- 5.8 










5 -8 


+ 4.5 


+ 1.2 


-2 -6 


- as 1 + 0.7 ' 


-6 -7 


+ 2.8 


- 4.0 


-8 


-8 


+ 3.6 


0.0 


6 -8 


+ 12.7 


+ 1.2 


-1 -6 


- 5.2 


- 5.1 


-4 -7 


0.0 


+ 0.8 


-7 


-8 


+ 6.9 


- 10.9 


7 -8 


+ 6.9 


+ 10.9 


-6 


0.0 


0.0 


-3 -7 


- 0.9 


- 2.9 


-6 


-8 


+ 12.7 


- 1.2 


8 -8 


+ 3.6 


0.0 


1 -6 


+ 5.6 


+ 5.8 


-2 -7 


+ 0.5 - 1.1 1 




















RetaiThed Terms 


of 


the Forces, 






Xi 


¥i 


Zi 


• 


V 


Xi 


Yi 


Zi 


COS 


sin 


cos 


sin 


cos 


sin 


cos 


sin 


cos 


sin 


cos 


sin 





— 


1273.1 


0.0 


+ 66.7 


0.0 


- 550.6 


0.0 


3 


-2 


+ 441.0 


- 143.0 


- 64.6 + 280.1 


+ 356.7 


+ 329.5 


1 


+ 


3707.8 


- 224.0 


- 180.6 


+ 3507.2 


+1456.4 


+1647.6 


4 


-2 


+ 149.4 


- 0.2 


- 20.1 + 61.7 


+ 62.3 


+ 85.8 


2 


+ 


271.4 


+ 29.2 


- 61.0 


+ 290.6 


+ 40.6 


+ 95.4 


5 


-2 


+ 23.8 


- 9.4 


+ 11.4 


+ 46.9 


+ 25.9 


+ 23.3 


3 


+ 


55.1 


- 36.5 


+ 43.1 


+ 22.9 


+ 33.4 


+ 6.7 


6 


-2 


+ 15.9 


- 12.6 


- 16.2 


- 13.1 






4 


+ 


11.6 


- 7.4 


+ 7.5 


+ 49.4 


+ 7.8 


+ 7.2 


7 


-2 


- 1.5 


+ 7.7 


+ 24.8 


+ 11.7 






5 


+ 


1.2 


- 3.8 


- 13.1 


- 31.6 






8 


-2 


- 1.2 


- 3.9 


- 15.0 


- 0.1 






6 


+ 


1.8 


0.0 


+ 27.5 


+ 27.0 










• 












7 


— 


1.1 


- 1.1 


- 34.1 


- 14.4 






-3 


-3 


- •y.o 


+ 2.2 


+ 4.8 


- 8.8 






8 


+ 


1.0 


0.0 


+ 19.0 


0.0 






-2 


-3 


+ 0.3 


- 1.2 


- 4.2,+ 6.7 




. 


















-1 


-3 


- 18.7 


- 6.4 


- 3.9 


+ 10.7 






-5 -1 


+ 


17.4 


+ 4.8 


- 3.7 


+ 1.3 









-3 


+ 174.3 


+ 60.3 


+ 50.5 


- 170.8 


+ 60.7 


- 32.6 


-4 -1 


— 


19.3 


+ 1.9 


+ 7.6 


3.4 






1 


-3 


-1941.3 


+ 366.8 


+ 416.3 


+1909.7 


- 252.3 


+ 387.8 


-3 -1 


+ 


21.1 


+ 4.8 


+ 2.7 


+ 0.2 






2 


-3 


+5242.4 


- 845.2 


- 952.4 


-5136.7 


+ 641.7 


-935.1 


-2 -1 


+ 


6.9 


+ 79.6 


+ 72.3 


- 30.3 


+ 33.6 


+ 6.8 


3 


-3 


+ 715.6 


- 40.8 


- 93.8 


- 902.6 


- 120.1 


- 238.2 


-1 -1 


— 


298.8 


- 56.1 


- 5.9 


+ 290.8 


- 156.4 


+ 148.1 


4 


-3 


+ 264.1 


- 91.3 


- 46.1 


- 51.2 


+ 165.7 


+ 109.8 


-1 


+ 


2521.5 


- 9.2 


- 274.4 


- 2319.6 


+ 946.0 


-1066.3 


5 


-3 


+ 87.3 


- 26.9 


- 21.3 


+ 18.1 


+ 55.0 


+ 49.7 


1 -1 


— 


1310.8 


+ 148.2 


+ 146.4 


+ 239.5 


- 712.7 


- 136.9 


6 


-3 


+ 17.8 


- 4.8 


+ 1.9 


+ 2.3 


+ 19.4 


+ 13.1 


2 -1 


+ 


1100.5 


- 208.3 


- 83.6 


+ 1111.2 


+ 742.9 


+ 793.3 


7 


-3 


+ 6.8 


- 8.8 


- 4.0 


+ 7.0 






3 -1 


+ 


170.0 


- 14.4 


- 22.2 


+ 189.0 


+ 93.1 


+ 126.7 


8 


-3 


- 4.9 


+ 4.3 


- 1.6 


- 5.4 


• 




4 -1 


+ 


60.0 


- 18.5 


+ 4.5 


+ 46.9 


+ 30.0 


+ 21.6 


















5 -1 


— 


7.9 


- 0.8 


+ 11.4 


+ 5.3 






-2-4| 


+ 13.6 


- 8.6 


- 0.4 


+ 1.3 


+ 18.5 


+ 1.5 


6 -1 


+ • 


15.4 


- 11.4 


- 4.1 


+ 7.7 






-1 


-4 


- 9.4 


+ 16.2 


+ 2.6 


- 3.2 


- 15.4 


+ 0.5 


7 -1 


+ 


6.9 


+ 8.3 


+ 1.6 


6.8 






-4 


- 48.1 


- 24.1 


- 10.2 


+ 48.4 


- 9.5 


+ 5.2 


8 -1 


+ 


2.2 


- 6.5 


+ 5.4 


+ 2.1 






1 -4 


+ 327.4 


+ 6.0 


- 14.5 


- 315.9 


+ 68.2 


- 58.1 


















2-4 


-1374.1 + 339.5| 


+ 377.7 


+1337.6 


- 155.1 


+ 274.1 


-4 -2 


— 


13.7 


+ 1.2 


- 0.4 


+ 25.9 






3 


-4 


+2445.8 


- 526.9 


- 576.6 


-2365.7 


+ 290.1 


- 439.8 


-3 -2 


+ 


11.1 


- 2.4 


- 7.6 


- 24.2 






4 


-4 


+ 567.4 


- 81.7 


- 116.2 


- 665.3 


- 46.3 


- 162.0 


-2 -2 


— 


4.1 


+ 9.2 


+ 22.3 


+ 12.4 






5 


-4 


+ 204.0 


- 65.5 


- 43.2 


- 113.2 


+ 75.9 


+ 24.5 


-1 -2 


+ 


129.5 


+ 109.7 


+ 86.1 


- 135.9 


+ 63.1 


- 15.3 


6 


-4 


+ 39.5 


- 14.6 


- 13.4- 21.1 1 


+ 31.9 


+ 22.7 


-2 


— 


3339.0 


+ 294.1 


+ 393.6 


+ 3296.3 


- 428.2 


+ 589.8 


7 


-4 


+ 31.2- 17.1 


- 8.3 


+ 1.9 






1 -2 


+1 


0242.4 


-1049.0 


-1302.1 


-10042.0 


-1317.9 


-1799.0 
- 271.8 


8 -4| 


- 13.2+ 6.9 


- 2.7 


- 16.7 






2 -2 


+ 


337.0 '+ 64.6| 


+ 21.0 


- 820.1 


- 303.0 




1 













8 







Retained Terms of the Forces. 














Xi 


Yi 


Zi 




Xi 


Yi 


z, 1 


cos 


sin 


cos 


gin 


COB 


+ 


sin 
2.5 


cos 


sin 


cos 


sin 


cos 


sin 1 


-1 -5 


- 2.3 


+ 


4.6 


^ 


5.3 


+ 0.9 


+ 


33.3 


9 -6 


— 


21.0 


+ 


3.9 


— 


3.9 


__ 


20.8 










-5 


+ 2.5 


— 


2.0 


+ 


8.7 


- 1.4 


— 


14.4 


— 


0.2 




























1 -5 


- 46.7 


— 


0.6 


— 


11.0 


+ 44.7 


— 


8.7 


+ 


7.8 


1 -7 


— 


6.0 


— 


13.2 


+ 


4.5 


+ 


6.9 


+ 


32.3 


— 


1.5 


2 -5 


+ 261.0 


— 


44.9 


— 


43.0 


- 252.9 


+ 


44.5 


— 


52.1 


2 -7 


+ 


21.2 


+ 


10.3 


— 


4.7 


— 


12.5 


— 


2.5 


— 


1.0 


3 -5 


- 804.6 


+ 


266.5 


+ 276.2 


+ 790.9 


— 


81.9 


+ 


168.1 


3 -7 


— 


53.6 


+ 


1.2 


+ 


12.9 


+ 


42.8 


— 


5.0 


+ 


8.0 


4 -6 


+1037.1 


— 


288.1 


— 


306.7 


-1000.8 


+ 


122.8 


— 


191.4 


4 -7 


+ 


133.3 


— 


42.0 


— 


51.5 


— 


120.4 


+ 


13.2 


— 


27.0 


5 -5 


+ 385.4 


— 


77.0 


— 


96.6 


- 407.2 


— 


18.8 


— 


95.6 


5 -7 


— 


223.6 


+ 


106.2 


+ 113.6 


+ 229.7 


— 


15.5 


+ 


50.5 


6 -5 


+ 119.0 


— 


37.1 


— 


38.9 


- 98.4 


+ 


31.6 


— 


2.1 


6 -7 


+ 


149.6 


— 


58.5 


— 


79.5 


— 


171.2 


+ 


17.1 


— 


30.6 


7 -5 


+ 40.8 


— 


29.4 


— 


3.0 


- 37.0 


+ 


18.4 


+ 


5.6 


7 -7 


+. 


148.6 


— 


45.4 


— 


39.2 


— 


83.3 


— 


0.5 


— 


20.7 


8 -5 


- 16.9 


+ 


9.9 


— 


19.2 


- 29.0 










8 -7 


+ 


23.1 


— 


7.7 


— 


6.3 


— 


45.1 










9 -5 


- 12.4 


+ 


3.4 


— 


3.3 


- 12.3 










9 -7 


— 


9.7 


+ 


12.0 


— 


11.9 


— 


9.7 










-2 -6 


- 11.2 


+ 


6.2 


_ 


19.4 


- 19.9 










-1 -8 


+ 


5.2 


_ 


17.5 


.^ 


17.5 


__ 


5.1 










-1 -6 


+ 1.7 


— 


7.3 


+ 


24.2 


+ 11.4 


— 


30.3 


— 


2.1 


-8 


+ 


2.8 


+ 


19.0 


+ 


J8.9 


— 


1.2 


+ 


24.0 


+ 


1.6 


-6 


+ 0.3 


+ 


9.0 


— 


26.7 


+ 0.5 


+ 


25.7 


+ 


1.6 


1 -8 


— 


12.6 


— 


16.4 


— 


16.2 


+ 


9.1 


— 


37.9 


+ 


1.9 


1 -6 


+ 0.4 


^" 


6.0 


+ 


25.9 


- 16.4 


— 


8.3 


— 


2.4 


2 -8 


+ 


13.1 


+ 


12.6 


+ 


12.4 


— 


12.1 


+ 


16.8 


— 


2.3 


2 -6 


- 37.7 


+ 


10.0 


— 


15.1 


+ 64.1 


— 


9.8 


+ 


11.9 


3 -8 


— 


8.7 


— 


7.3 


— 


6.3 


+ 


9.4 


— 


1.9 


+ 


0.8 


3 -6 


+ 175.4 


— 


55.6 


— 


44.8 


- 205.8 


+ 


25.6 


— 


43.0 


4 -8 


— 


9.8 


+ 


9.3 


+ 


9.4 


+ 


10.2 


— 


0.7 


+ 


3.1 


4 -6 


- 424.6 


+ 


177.8 


+ 181.2 


+ 459.3 


— 


38.5 


+ 


98.1 


5 -8 


+ 


62.0 


— 


26.9 


— 


2R.9 


— 


66.9 


+ 


5.6 


— 


13.7 


5 -6 


+ 411.7 


— 


136.9 


— 


159.7 


- 422.5 + 


49.2 


— 


80.5 


6 -8 


— 


93.5 


+ 


50.5 


+ 


58.8 


+ 


104.6 


— 


3.6 


+ 


21.0 


6 -6 


+ 228.2 


— 


55.2 


— 


50.9 


- 192.7 - 


5.7 


— 


47.5 


7 -^ 


+ 


42.2 


— 


4.2 


— 


16.6 


— 


72.7 


+ 


5.3 


— 


9.6 


7 -6 


+ 89.2 


— 


22.3 


— 


54.2 


- 93.4 + 


10.5 


— 


8.1 


8 -« 


+ 


24.9 


— 


38.7 


— 


19.7 


— 


10.6 










8 -^ 


- 22.5 


— 


8.9 


+ 


0.8 


- 50.31 



































r^i?^ = a:,X,+y,Y, 

dxx , V dy\ 



For the computation of 
and 
we have the above series for Xi and ^i with reversed signs, and 



T=^r-ij+Yr-fi 



dxi 
'dt 



= —4.07365 sin M 

—0.87270 sin 2 M 
—0.21058 sin 3 Jf 
—0.05352 sin 4 M 
—0.01402 sin 5 M 
—0.00375 sin 6 if 
—0.00100 sin 7 M 



^ = +0.00003 + 4.02388 cos M 

+ 0.86552 cos 2 Jfcf 
+ 0.20922 cos 3 ilf 
+ 0.05330 cos 4 if 
4- 0.01392 cos 5 if 
-|- 0.00380 cos 6 M 
+ 0.00112 cos 7 if 



+ 0.00028 cos 8 M 

These multiplications furnish us now finally the material for the formation of the difierential equation for 
r® d r, namely, of 

tSQil + ^^^J"^> (r^ a r) = r^ ir + 2 /c^ r** (^ < = J*. 



df 






9 







% 


• 






Terms of 2 retained for integration. 












• 


f' 


cos 


sin 


• 

h 


t' 


cos 


sin 


• 


V 


cos 


sin 


• 


t' 


cos 


sin 








+ 


9109.8 


0.0 


-1 


-2 


- 214.7 


- 225.4 


4 


-4 


+8063.0 


-1850.3 


6 


-6 


+1013.5 


-350.0 


1 





— 


7631.9 


+ 561.6 





-2 


+ 3113.6 


+ 435.3 


5 


-4 


+3015.7 


- 525.3 


7 


-6 


+ 677.6 


-202.9 


2 





— 


13.2 


- 877.8 


1 


-2 


-49502.2 


+5429.7 


6 


-4 


+ 950.1 


- 251.7 


8 


-6 


+ 362.8 


--129.7 


3 





— 


31.4 


- 142.2 


2 


-2 


+51251.5 


-6036.5 


7 


-4 


+ 195.6 


- 60.2 










4 





+ 


27.6 


- 5.0 


3 


-2 


+ 8109.5 


- 413.2 










1 


-7 


+ 28.7 


+ 53.2 


5 





— 


35.0 


- 18.2 


4 


-2 


+ 1518.4 


- 473.2 


1 


-^ 


+ 77.2 


- 40.9 


2 


-7 


+ 157.4 


- 70.3 


6 





+ 


30.0 


- 2.2 


5 


-2 


+ 431.0 


- 90.6 


2 


-5 


- 638.2 


- 18.8 


3 


-7 


+ 130.5 


+ 2.7 


7 





— 


29.5 


+ 21.7 










3 


-5 


+1875.3 


- 439.1 


4 


-7 


- 307.2 


+ 62.4 


8 





+ 


14.1 


- 44.6 





-3 


- 208.1 


- 119.9 


4 


-5 


-3827.3 


+1280.4 


5 


-7 


+ 609.7 


-243.4 


9 





+ 


3.0 


+ 20.6 


1 


-3 


+ 5649.5 


+ 26.7 


5 


-5 


+2916.8 


- 851.0 


6 


-7 


- 783.2 


+388.8 


p 










2 


-3 


-15678.7 


+3104.7 


6 


-5 


+1588.1 


- 379.9 


7 


-7 


+ 289.9 


-139.6 


-2 


—1 


+ 


10.1 


- 80.2 


3 


-3 


+20761.9 


-3605.4 


7 


-5 


+ 501.0 


- 127.7 


8 


-7 


+ 365.4 


-123.3 


-1 


—1 


+ 


578.1 


+ 686.0 


4 


-3 


+ 5454.1 


- 6284 


8 


-5 


+ 192.7 


- 75.1 













—1 


— 


3520.7 


- 11.5 


5 


-3 


+ 1309.6 


- 321.7 










2 


-8 


+ 101.2 


+120.2 


1 


—1 


+16549.2 


-1084.2 


6 


-3 


+ 330.1 


- 126.3 





-6 


- 29.7 


- 74.4 


3 


-8 


+ 105.6 


+ 96.9 


2 


—1 


— 


2803.0 


+ 760.2 










1 


-6 


+ 92.7 


+ 123.8 


4 


-8 


- 28.5 


- 31.8 


3 


~1 


— 


261.1 


- 495.8 





-4 


+ 67.5 


+ 56.3 


2 


-6 


+ 370.1 


+ 256.6 


5 


-6 


- 85.7 


+ 51.5 


4 


—1 


— 


99.9 


- 116.9 


1 


-4 


+ 399.3 


+ 32.9 


3 


-6 


- 440.1 


+ 30.6 


6 


-6 


+ 272.2 


-123.8 


5 


—1 


+ 


34.7 


- 45.4 


2 


-4 


+ 3281.9 


- 388.5 


. 4 


-6 


+1089.6 


- 344.7 


7 


-8 


- 311.7 


+153.9 












3 


-4 


- 7965.4 


+2071.6 


5 


-6 


-1794.8 


+ 723.2 


8 


-8 


+ 119.9 


+ 17.6 



For the computation of the coefficients of integration we have, — 

log li 3.008587 log po 9.87395n 

« pi 0.35822 

2.475808 « p^ 9.88308 

« jDg 8.58950 
« ;?4 7.86982 
« ps 7.19033 



log yl 

« /i + 0.256752 
« ,i' + 9.724023 



/i 1.806142 

/i' 0.529691 « p^ 6.54407 

p and q are the coefficients in the series for Xx and yi. 



log^i 0.34788 

« q^ 9.37951 

" ^3 8.58670 

« q^ 7.86747 

« qs 7.19083 

« 9, 6.54407 



log 



ah 



9.288603 



log - 9.743248 



log -!- 9.031851 



^ 1.806142 


/ 


0.529691 


2^ 3.612284 


2 m' 


1.059382 


3/* 5.418426 


3^' 


1.589073 


4^ 7.224568 


4/ 


2.118764 


6yL 9.030710 


byJ 


2.648455 


6;* 10.836852 


%p! 


3.178146 


7/i 12.642996 


7/*' 


3.707837 


8fi 14.449186 


8 m' 


4.237528 


9;* 16.255278 


9 m' 


4.767219 


10 /i 18.061420 






11 /i 19.867562 







II ■ II 11 ■!■! 



10 



Log of the ^ JSntwtcielungS'FactorenJ 



+«, +1 



,-+4and»-4J^-'^^ 



+4, +«i -I 
0, —4 +1, —6 

4.68480n 7.33105 7.30661n 



• • • • 

• • • • 



.• + 8aad»-3{ i^. t 



+«, +4,-1 +».-«.... 

6.02698n 7.92534 7.9b573n 6.40380» 



t -j- 2 and i 



-'K 



0, -2 

54206 



+«, -I 

+1, -8 

8.52827n 



+i, -2 

+8, -4 

7.01565fi 



+«, -« . 

+S, -^ . 

5.66881n 



,- + land»_lj^}j^^- 



+8, -1 
+1. -2 

9.19653n 



+8. -2 

7.65594n 



+4, -« . 
+3, -4 . 

6.28942n 



-• \ +1, -1 +«, -2 +8. -8 +4» — I . 

|9.98970» 8.35223» 6.94297n 5.62793n 
The numbers above the logarithms are those which constitute ±x in t ±x. 



Specimen of the Tables of Divisors. 


For the Glass i' — 0. 






—4 


—8 


-2 


-1 





+1 


+2 


+8 


+4 


-W 


t 

+• 


+r 


+6 


+9 


-6 




9*14119,1 


9*36618^ 


9*44331» 


9*74835m 


00 


9*74335 


9*44331 


9*36618 


9*14119 9*04436 


8*96510 


8*89815 


8*84016 


8*78900 


9-04498» 


8*18U7 


8*81041 


8*48649 


8.J875S 


8*08856), 


8*78758. 


8*48649. 


8*81041. 














-4 


»• 141 19m 




8.40733 


8*58840 


8*88444 


8*38338n 


8*88444. 


8*58340. 


8*40783. 


8*38388. 












-8 


9.96613n 






8*70884 


9*00988 


9*58336» 


9*00988. 


8*70684. 


8*63336. 


8*40733. 


8*31041. 










-3 


9-44391m 








9*18646 


8*88443» 


9.18566. 


8*88443. 


8*70634. 


8*58840. 


8*48649^ 


8*40731. 








-1 


9.74335» 










9*48650. 


9*48650^ 


9*18546. 


9*00988. 


8*88444. 


8*78753. 


8*70885. 


8*64140. 









00 












9*48650. 


8*88443. 


8*58336. 


8*38336. 


8*08856. 


7*98090. 


7*79680^ 


7*68033. 




+1 


9-7483A 














9*18546 


9*00988 


8*88444 


8*78758 


8*70635 


8*64140 


8*58341 


8*53395 


+a 


9.44331 
















8*70634 


8*58840 


8*48649 


6*40731 


8*34036 


8*38337 


8*38131 


+8 


9*36618 


















8*40783 


8*31041 


8*38193 


8*16438 


«• 10639 


8*05518 


+4 


9-14119 














• 






8*16647 


8*10639 


8*08934 


7*98135 


7*98019 


+5 


9*04438 






















8*00988 


7*94348 


7*88444 


7*83338 


+6 


8*96510 
























7*86335 


7*80536 


7*75410 


+7 


8*89815 


























7*73831 


7*68715 


+8 


8*84016 




























7*63916 



When for this class t' = 0, one of the divisors in 



, becomes zero we have to put down 



(i — It) /i . (i — k!) /i 
the negative square of that divisor which retains a real value. This table of the divisor for i' = and for the 

coefficients of integration /? (i -j- x) is changed into the table of the divisors for /{ {% -\- x) by squaring all the 

numbers and bj adding to the logarithms of the squares log {c -f- &) fi. Excepted herefrom are the terms for 

which c or & becomes zero. Those terms are to be multiplied by -7- or — . 

^ "^ C'fJi Cfl 



11 



Specimen of the TaUes of the Coefficients of Integration. 

i' — 0. 




/-4 
+<H)0006 


/-8 


/-a 


/-I 


/o 


/+! 


/+a 


/+-8 


/+-4 


/+6 


/+« 


/+-7 


2* 


t =*o 


-H).00081 


+04)0089 


-0*03583 


+0.80113' 


-0*03683 


+0*00083 


+0*00081 


+0*00008 








+0'36390 


t-i 




-O'OOOU 


-0*00084 


-0*00800 


-0*03633 


+0*07717* 


+0*08063 


+0*00497 


+0*00078 


+0*00016 






+0*07846 


i s3 






-0.00009 


-0-00086 


+0*00083 


+0*00063 


-0*09981* 


-0*00871 


-0*00078 


-0*00016 


-0*00004 




-0*07366 


t »8 








-0*00014 


+0*00081 


+0*00427 


-0*00371 


-0.08879* 


-0*00091 


-0*00019 


-0*00004 




-0*08930 


t "4 










+0*00008 


+0*00078 


-0*00078 


-0-00091 


-0.02069* 


-0*00080 


-0*00007 




-0*03179 


f »6 












+0*00016 


-0*00016 


-0*00019 


-0*00080 


-0*01383* 


-0*00013 




-0*01848 


* -6 
















-0*00004 


-0*00007 


-0*00013 


-0*00877* 




-0*00900 






1 




1 
















-0*00689* 


-t)*00639 



In such a table it is only necessary to compute the values on one side of the diagonal line of asterisks, since 
the values appear on both sides arranged in the same manner as [a b"], [a c], [b c], with respect to [a a], [h h"] 
in the method of least squares. By means of the horizontal sums ^ the coefficients are checked because of 



» om — OO , . , . + CO 



ab 



* . « ( <7i I ^ I 85s 

t (i + 1, i') (i-1, t') ■<■ (i+2, i') (t-.2, ,') -r (, .|. 3, ,v^ 0-3,1') 



II 


• 


t' 


cos 


Bin 


• 


t' 


cos 


sin 


• 


t' 


cos 


sin 


• 


1' 


cos 


sin 








+ 41.67^ 




0.0 





-2 


+ 9933.9 


- 754.7 


5 


-4 


- 61.9 


+11.5 


-1 


-7 


+ 1.3 


- 3.6 


1 





-125.63^ 


-3697.52* 


1 


-2 


-12287.5 


+1166.2 


6 


-4 


- 15*0 


+ 3.9 





-7 


+ 7.9 


- 21.8 


2 





- 13.46* 


— 


397.69* 


2 


-2 


-21290*5 


+2442.7 


7 


-4 


- 1.8 


+ 0.5 


1 


-7 


+ 64.1 


-210.9 


3 





- 2*61< 


— 


64.08* 


3 


-2 


- 2306.4 


+ 229.2 






* 




2 


-7 


- 31.3 


+ 22.5 


4 





0.0 


— 


12.23* 


4 


-2 


- 371.6 


+ 50.1 


-1 


-5 


+ 2.2 


- 0.7 


3 


-7 


+148.5 


+ 87.3 


5 





0.0 


— 


2.51* 


5 


-2 


- 46.1 


+ 6.0 





-5 


+ 14.2 


- 4.0 


4 


-7 


+ 51.3 


+ 3.4 




















1 


-5 


+127.2 


- 9.3 


5 


-7 


- 19.2 


+ 10.6 








+ 2936.7 




0.0 


-3 


-3 


1.0 


- 0.6 


2 


-5 


-138.4 


-29.3 


6 


-7 


+ 17.3 


- 8.0 


1 





- 969.2 


+ 


19.8 


-2 


-3 


- 44.5 


- 3.4 


3 


-5 


-433.7 


+80.6 


7 


-7 


- 3*7 


- 1.9 


2 





- 210.4 


+ 


105.3 


-1 


-3 


- 276.0 


- 23.1 


4 


-5 


+184.0 


-^.4 


8 


-7 


- 3.3 


+ 1.1 


3 





- 25.8 


+ 


11.2 





-3 


- 2694.8 


- 192.4 


5 


-5 


- 77.9 


+21.7 






• 




4 





- 6.2 


+ 


1.2 


1 


-3 


- 3380.5 


+1118.1 


6 


-^ 


-25*7 


+ 5.8 





-6 


+ 1.7 


+ 2.1 












2 


-3 


+18286.1 


-3229.5 


7 


-5 


- 5*8 


+ 1.5 


1 


-8 


+ 13.0 


+ 15.7 


-3 


—1 


- 15.5 


- 


3.7 


3 


-3 


- 155.7 


+ 30.7 


8 


-5 


- 1*4 


0.0 


2 


-8 


+ 14.3 


+ 22.4 


-2 


—1 


- 111.9 


— 


15.2 


4 


-3 


+ 17.1 


- 13.6 










3 


-8 


+ 32.1 


+ 24.5 


-1 


—1 


- 969.8 


- 


293.3 


5 


-3 


+ 3.3 


- 0.4 


-1 


-6 


+ 0.2 


+ 1.2 


4 


-8 


+ 13.9 


+ 12.8 





—1 


- 4613.1 


+ 


328.3 


6 


-3 


9.6 


+ 2.4 





-6 


+ 6.3 


+17.9 


5 


-8 


+ 5.6 


- 1.1 


1 


-1 


+10401.0 


- 


584.0 










1 


-6 


- 27.4 


+16.8 


6 


-8 


- 6.3 


+ 3.1 


2 


—1 


+ 2177.7 


— 


221.7 


-2 


-4 


+ 1.5 


- 0.4 


2 


-6 


+ 28.2 


+51^ 


7 


-8 


+ 4.5 


- 2.3 


3 


—1 


+ 291.9 


+ 


3.1 


-1 


-4 


+ 4.6 


- 2.3 


3 


-6 


+279.0 


+42.3 


8 


-8 


- 1.2 


0.0 


4 


-1 


+ 52.3 


— 


0.4 





-4 


+ 32.0 


- 33.7 


4 


-6 


- 55.1 


+30.5 




















1 


-4 


- 716.1 


+ 96.8 


• 

5 


-6 


+ 59.2 


^21.5 


6 


-9 


+ 1.5 


- 0.9 


-3 


-2 


+ 8.3 


+ 


1.5 


2 


-4 


+ 2107.7 


- 145.9 


6 


-6 


- 17.3 


+ 6.0 


7 


-9 


- 2.2 


+ 1.0 


-2 


-2 


+ 142.5 


- 


2.2 


3 


-4 


+ 1322.8 


- 288.0 


7 


-6 


- 7*9 


+ 2.4 


8 


-9 


+ 0.4 


- 0*8 


-1 


-2 


+ 980.0 


+ 


17.4 


4 


-4 


- 264.9 


+ 66.3 


8 


-6 


- 2.8 


+ 1.0 


9 


-9 


- 0.1 


0.0 



For the formation of the differential equations for 1^ and tji it is necessary to multiply r^ dr with 
-^Xiand^yi. 



12 



3ic» 






xi = + 1.04488 + 5.01118 cos M 

+ 3.00130 cos 2 3f 
+ 1.38657 cos3Jf 
4- 0.56905 cos 4 3f 
+ 0.21828 cos 5 if 
+ 0.08089 cos 6 if 
+ 0.03161 cos 7 if 
+ 0.00979 cos 8 if 

Having performed these multiplications we obtain for integration 



+ 4.39501 sin M 

+ 2.81725 sin 2 3f 
+ 1.33137 sin 3 if 
■j- 0.55228 sin 4 M 
+ 0.21259 sin 5 if 
+ 0.07719 sin 6 if 
+ 0.02454 sin 7 if 



and simply 






• 


I' 


ll 


2 


V\ 


2 




i' 


€i 


2 


Vi 


2 


COS 


sin 


COB 


sin 


cos 


sin 


cos 


sin 








- 293.0^ 


0.0 


- 8731.9* 


0.0 


4 


-1 


+ 9901.6 


- 687.9 


+ 639.9 


+ 9298.1 


1 





- 157.8< 


+ 878.7^' 


- 6465.1* 


+ 28.9* 


5 


-1 


+ 4485.2 


- 293.2 


+ 293.5 


+ 4324.0 


2 





- 300.4« 


- 7176.5< 


+ 5387.1* 


- 241.4* 


6 


-1 


+ 1848.4 


- 128.2 


+ 108.6 


+ 1792.8 


3 





- 204.0< 


- 5548.U 


+ 4985.9* 


- 187.2* 


7 


-1 


+ 707.7 


- 35.2 


+ 42.0 


+ 685.0 


4 





- 103.3< 


- 2019-% 


+ 2747.8* 


- 98.1* 














5 





- 44.5< 


- 1300.9f 


+ 1255.3* 


- 42.8* 


-5 


-2 


+ 642.1 


+ 12.6 


+ 10.6 


- 722.2 


6 





- 17.7< 


- 525.2^ 


+ 523.1* 


- 16.7* 


-4 


-2 


+ 1486.2 


+ 29.1 


+ 24.1 


- 1432.4 


7 





- 6.U 


- 205.2< 


+ 214.3* 


5.8* 


-3 


-2 


+ 2815.4 


+ 106.1 


+ 100.8 


- 2580.8 


8 





2^ 


- 86.7« 


+ 72.6* 


- 2.2* 


-2 


-2 


+ 2684.3 


+ .452.4 


+ 471.5 


- 1797.5 


9 





1.W 


- 29.0* 


+ 9.4* 


0.3* 


-1 


-2 


- 7484.1 


+ 1745.8 


+ 1767.9 


+10518.1 


10 





O.W 


3.9* 


+ 1.6* 


0.0 





-2 


-54730.2 


+ 6308.1 


+ 6527.9 


+64290.9 






Check. 




Chi 


BCK. 


1 


-2 


-33213.1 


+ 4804.2 


+ 6058.7 


+63561.3 


lOo/Jo+i- 


^<Pm--^'7. 


^^-^m^+O^ 


-+0.2 


--1.3 


2 


-2 


-43437.6 


+ 5071.7 


- 911.5 


- 7514.1 














3 


-2 


-67573.3 


+ 7582.9 


- 6459.1 


-56034.2 








- 1018.5 


0.0 


+ 266.3 


0.0 


4 


-2 


-436^.0 


+ 4902.5 


- 4521.2 


-40231.6 


1 





+15182.5 


- 28.1 


+ 162.6 


+15375.4 


5 


-2 


-21547.8 


+ 2409.7 


- 2290.0 


-20489.0 


2 





+ 5564.4 


+ 173.9 


- 34.7 


+ 5736.0 


6 


-2 


- 9236.7 


+ 1028.4 


- 1022.1 


- 8963.1 


3 





+ 1767.9 


+ 254.2 


- 196.5 


+ 1794.1 


7 


-2 


- 3643.3 


+ 418.6 


- 375.7 


- 3553.1 


4 





+ 493.1 


+ 187.1 


- 172.2 


+ 546.1 


8 


-2 


- 1396.3 


+ 152.9 


- 165.9 


- 1351.0 


5 





+ 117.3 


+. 92.0 


- 105.0 


+ 88.9 














6 





+ 27.6 


+ 40.7 


- 12.6 


+ 52.6 


-4 


-3 


- 651.5 


- 85.0 


- 81.9 


+ 655.5 


7 





+ 12.2 


+ 15.1 


- 50.0 


- 14.3 


-3 


-3 


- 1374.1 


- 208.3 


- 196.8 


+ 1267.2 














-2 


-3 


- 1941.2 


- 493.8 


- 469.4 


+ 1623.6 


-5 


—1 


- 406.2 


- 85.9 


- 90.4 


+ 427.5 


-1 


-3 


+ 389.6 


- 1075.9 


- 986.1 


- 1536.3 


-4 


—1 


- 982.6 


- 212.8 


- 197.2 


+ 914.4 





-3 


+15466.8 


- 2231.2 


- 1968.7 


-19070.7 


-3 


—1 


- 1719.4 


- 439.9 


- 409.9 


+ 1568.1 


1 


-3 


+32924.0 


- 7039.1 


- 6188.3 


^4406.5 


-2 


—I 


- 1636.9 


- 655.5 


- 551.2 


+ 1006.6 


2 


-3 


+11266.3 


- 1666.8 


- 3073.1 


-16238.7 


-1 


—1 


+ 4032.3 


- 612.7 


- 215.2 


- 6026.3 


3 


-3 


+39386.4 


- 6595.6 


+ 5534.2 


+32608.6 





—1 


+24638.8 


- 2220.4 


- 1199.6 


-30750.9 


4 


-3 


+24184.2 


- 4154.3 


+ 3749.3 


+22344.9 


1 


—1 


+ 2392.2 


- 642.0 


- 633.8 


-16574.1 


5 


-3 


+11285.6 


- 1951.6 


+ 1832.9 


+10799.1 


2 


~1 


+22618.3 


- 1611.4 


+ 943.3 


+16076.1 


6 


-3 


+ 4654.2 


- 807.3 


+ 782.0 


+ 4512.8 


3 


-1 


+18183.6 


- 1301.6 


+ 1150.8 


+16159.8 


7 


-3 


+ 1770.4 


- 314.5 


+ 294.3 


+ 1739.2 



13 



« 

• 


t' 


li 


2 






Vi 


2 


• 


if 




6 


S 






Vi 


2* 




cos 


sin 


cos 


sin 


cos 


sin 


008 


sin 1 


8 


-3 


+ 643.7 


.. 


106.8 


+ 


106.7 


+ 636.1 


2 


-6 


+ 


584.2 


+ 


270.1 


+ 


47.8 


^» 


556.3 










• 








3 


-6 


+ 


437.0 


+ 


203.4 


— 


151.2 


— 


126.5 


-2 


-4 


+ 310.6 


— 


68.2 


— 


56.7 


- 286.9 


4 


-6 


+ 


358.0 


+ 


366.4 


— 


36.9 


+ 


995.9 


-1 


-4 


+ 810.7 


— 


101.6 


— 


103.4 


- 799.2 


5 


-6 


+ 


709.5 


+ 


42.1 


— 


309.6 


~ 


87.7 





-4 


+ 2202.0 


— 


221.4 


— 


169.3 


- 2134.8 


6 


-6 


+ 


450.4 


— 


3.1 


— 


84.7 


+ 


71.9 


1 


-4 


+ 6730.5 


— 


729.0 


" 


615.5 


-6538.2 


7 


-6 


+ 


162.7 


+ 


5.0 


— 


73.3 


+ 


0.4 


2 


-4 


+ 1955.1 


— 


235.7 


- 


317.0 


-2674.6 






















3 


"4 


+ 7290.6 


— 


885.8 


- 


204.7 


+ 1960.0 


-2 


-7 


+ 


54.5 


— 


161.6 


— 


161.9 


— 


67.0 


4 


-4 


+ 6102.3 


— 


860.7 


+ 


698.4 


+ 4901.3 


-1 


-7 


+ 


151.6 


— 


346.6 


— 


304.2 


— 


128.3 


5 


-4 


+ 2681.5 


— 


386.5 


+ 


300.1 


+ 2412.3 





-7 


+ 


239.2 


— 


450.1 


— 


367.1 


— 


210.4 


6 


-4 


+ 906.7 


— 


113.1 


+ 


92.0 


+ 861.4 


1 


-7 


+ 


259.1 


— 


101.8 


+ 


234.0 


— 


144.9 


7 


-4 


+ 293.8 


— 


37.9 


+ 


14.6 


+ 267.7 


2 


-7 


+ 


602.1 


— 


30] .2 


+ 


692.7 


— 


249.8 


















3 


-7 


+ 


235.5 


— 


165.7 


+ 


292.0 


— 


25.8 


-1 


-5 


+ 23.6 


— 


23.9 


— 


30.9 


- 13.7 


4 


-7 


+ 


533.2 


+ 


74.6 


— 


117.3 


+ 


228.1 





-5 


- 124.0 


— 


35.9 


— 


13.9 


+ 166.0 


5 


-7 


+ 


140.3 


+ 


187.4 


+ . 


9.8 


+ 


518.6 


1 


-5 


- 770.1 


— 


13.7 


+ 


9.7 


+ 895.9 


6 


-7 


+ 


283.7 


+ 


4.4 




' 151.0 


— 


31.0 


2 


-5 


- 414.6 


+ 


12.5 


+ 


81.9 


+ 801.6 


7 


-7 


+ 


228.1 


~ 


28.0 


— 


54.4 


+ 


9.6 


3 


-5 


- 1078.9 


+ 


128w4 


+ 


243.3 


+ 400.4 






















4 


-5 


- 210.8 


— 


143.9 


— 


378.3 


- 1848.4 


-1 


-8 


+ 


49.6 


+ 


35.3 


+ 


32.3 


— 


47.1 


5 


-5 


- 18.1 


— 


108.7 


— 


24.7 


- 603.6 





-8 


+ 


85.2 


+ 


114.7 


+ 


104.7 


— 


75.5 


6 


-5 


- 169.1 


• 


27.5 


— 


32.8 


- 308.5 


1 


-8 


+ 


99.9 


+ 


107.1 


+ 


71.3 


— 


74.1 


7 


-5 


- 155.7 


- 


8.3 


— 


20.1 


- 207.0 


2 


-8 


+ 


166.9 


+ 


158.9 


+ 


46.6 


— 


73.9 


8 


-5 


- . 124.0 


+ 


25.8 


— 


33.9 


- 128.7 


3 


-8 


+ 


121.3 


+ 


131.4 


— 


50.9 


+ 


24.9 


















4 


-8 


+ 


123.3 


+ 


129.5 


— 


86.5 


+ 


104.0 


-1 


-6 


+ 71.7 


+ 


112.7 


+ 


134.3 


- 55.7 


5 


-8 


+ 


154.8 


+ 


65.2 


— 


107.3 


+ 


30.4 





-6 


+ 164.4 


+ 


183.6 


+ 


112.6 


- 154.6 


6 


-8 


— 


27.9 


+ 


89.5 


+ 


13.8 


+ 


155.1 


1 


-6 


+ 453.6 


+ 


265.6 


+ 


173.0 


- 434.8 


7 


-8 


+ 


57.3 


+ 


18.4 


— 


40.2 


— 


55.8 



The integration of the preceding three differential equations gives finallj the perturbations of the rectangu- 
lar co-ordinates. 



• 


if 


& 


i?i 


1 


cos 


sin 


N COS 


sin 


cos 


sin 








- 84.94^ 


0.0 


-1022.4W 


0.0 


+ 148.67* 


0.0 


1 





- 4.74t 


+4279.97^ 


-415440^ 


- 11.92* 


- 448.23* 


+ 493.85* 


2 





+ 25.65t 


+1241.89^ 


-1226.46* 


+ 24.98* 


- 48.01* 


+ 53.12* 


3 





+ 8.3W 


+ 325.86< 


- 322.92« 


+ 8.27* 


- 7.72* 


+ 8.56* 


4 





+ 2.50^ 


+ 86.2U 


- 85.92* 


+ 2.37* 


- 1.47* 


+ 1.63* 


5 





+ 0.€8t 


+ 22.98^ 


- 22.70* 


0.0 


- 0.31* 


+ 0.34* 


6 





+ 0.16t 


+ 6.19* 


- 6.02* 


0.0 


- 0.07* 


+ 0.08* 


7 





0.0 


+ 1.31« 


- 1.37* 


0.0 


0.0 


0.0 








-699.7 


0.0 


+ 75.5 


0.0 






1 





+1118.5 


- 5.6 


- 9.4 


+ 901.6 


- 202.6 


0.0 


2 





+ 463.6 


- 31.7 


+ 28.9 


+ 433.4 


+ 129.9 


+ 143.4 


3 





+ 100.7 


- 15.4 


+ 13.1 


+ 97.4 


+ 38.2 


+ 42.2 


4 





+ 23.3 


- 5.2 


+ 4.9 


+ 21.1 


+ 5.2 


+ 6.6 


5 





+ 5.8 


- 1.5 


+ 1.7 


+ 6.1 


+ 0.8 


+ 1.0 


6 





+ 0.8 


- 0.4 


+ 0.1 


+ 0.5 


+ 0.2 


+ 0.2 


-5 


-1 


+ 4.1 


+ 1.1 


+ 1.0 


- 4.0 


0.0 




-4 


-1 


+ 32.1 


+ 3.7 


+ 3.5 


- 32.4 


+ 0.8 


- 0.9 



14 



h »' 


& 


m 


£i 


1 


COB 


sin 


008 


sin 


cos 


sin 1 


-^ -i 


+ 122.3 


+ 11.8 


+ 11.8 


- 122.9 


+ 4.2 


«_ 


4.5 


-^ -1 


+ 494.5 


+ 26.8 


-1- 26.3 


- 491.7 


► + ' 22.7 


— 


26.9 


-1 -1 


+ 2206.5 


- 55.3 


- 72.4 


- 2188.4 


+ 226.2 


— 


2.36.6 


-1 


+ 7732.7 


- 671.7 


^ 325.3 


- 7809.7 


+ 428.1 


— 


312.4 


1 -1 


- 1340.7 


- 82.3 


0.9 


- 1289.8 


- 554.6 


+ 


231.4 


2 -1 


- 3739.2 


+ 227.2 


- 192.7 


~ 3658.9 


- 202.1 


— 


114.3 


3 -1 


- 1092.5 


+ 72.3 


- 70.3 


- 1081.8 


- 22.9 


— 


10.7 


4 -1- 


- 300.6 


+ 19.9 


- 19.6 


- 300.2 


4.2 


— 


1.6 


5 -1 


- 79.0 


+ 5.0 


5.4 


- 84.8 


0.6 


— 


0.3 


6 -1 


- 21.9 


+ 1.3 


-. 1.1 


- 20.7 








7 -1 


- 6.3 


0.0 


0.0 


- 6.1 


• 






-5 -2 


- 6.6 


0.2 


0.2 


+ 7.2 








-A -2 


- 50.0 


+ 1.9 


+ 2.0 


+ 52.5 








-3 -2 


- 192.0 


+ 7.5 


+ 7.8 


+ 192.5 


- 1.7 


+ 


2.1 


^2 -2 


•- 778.1 


+ 36.1 


+ 36.1 


+ 779.4 


9.2 


+ 


12.0 


-1 -2 


~ 3613.0 


+ 213.1 


+ 218.7 


+ 3500.3 


^ 72.0 


+ 


85.4 


-2 


-19149.5 


+ 2127.3 


+ 2083.7 


+19003.2 


- 428.6 


+ 


600.3 


1 -2 


- 8330.7 


+ 1305.0 


+ 754.2 


+ 9254.2 


+ 525.7 


— 


787.6 


2 -2 


+10930.4 


- 1169.0 


-1- 1065.5 


+10367.5 


+ 244.1 


— 


146.6 


3 -2 


+ 4932.9 


- 640.5 


+ 540.7 


+ 4849.2 


+ 3.7 


— 


46.1 


4 -2 


. + 1507.9 


- 166.7 


+ 166.1 


+ 1497.3 


+ 1.5 


— 


7.4 


5 -2 


+ 428.2 


- 47.6 


+ 47.9 


+ 432.3 


+ 0.3 


— 


1.4 


6 -2 


+ 122.5 


- 13.7 


+ 12.7 


+ 112.6 








7 -2 


+ 30.7 


3.5 


+ • 3.0 


+ 29.9 








8 -2 


+ 8.0 


0.8 


+ 0.9 


+ 7.7 








-4. -3 


1^ 


+ 3.0 


+ 3.8 


+ AS 


• 






-3 -3 


+ 65.9 


+ 3.6 


+ 3.5 


- 66.1 


+ 0.6 


— 


0.7 


-2 -3 


+ 245.3 


+ 13.5 


+ 13.2 


- 263.7 


+ 3.3 


— 


3.6 


-1 -3 


+ 1128.7 


+ 45.6 


+ 42.7 


- 1120.9 


+ 21.1 


— 


22.1 


-3 


+ 5T24.9 


+ 4.2 


- 15.3 


- 5630.2 


-¥ 187.9 


- 


208.4 


1 -3 


+ 9598.9 


- 2097.8 


- 1894.6 


- 9736.8 


+ 145.1 


— 


246.1 


2 -3 


-5031.4 


- 17.9 


+ 509.0 


- 2272.5 


- 842.5 


+ 


1273.3 


3 -3 


- 3779.0 


+ 589.8 


- 523.1 


- 3638.3 


- 69.4 


+ 


141.1 


4 -3 


- 1034.5 


+ 161.6 


- 156.4 


- 1022.7 


- 18.6 


+ 


16.8 


5 -3 


- 268.1 


+ 43.2 


- 42.6 


- 269.3 


3.7 


+ 


3.0 


6 -3 


- 80.4 


+ 13.6 


9.6 


- 56.7 


- 0.7 


+ 


0.5 


7 -3 


- 17.7 


+ 3.1 


3.0 


- 17.2 


■ 






8 -3 


4.0 


+ 0.7 


0.6 


3.9 








-4 -4 


1.1 






+ 1.1 








-3 -4 


+ 1.4 






1.3 








-2 -4 


3.2 


+ 1.4 


+ 0.9 


+ 2.7 


- 


- 


0.3 


-1 -4 


8.9 


+ 1.2 


+ 1.2 


+ 9.3 


+ 4.3 


— 


2.5 


-4 


+ 1.4 


- 12.1 


- 22.6 


4.0 


+ 27.9 


— 


21.9 


1 -4 


+ 1826.7 


- 182.2 


- 135.1 


- 1854.9 


+ 59.7 


— 


91.2 


2 -4 


+ 748.2 


- 120.8 


- 111.6 


- 32.3 


- 131.7 


+ 


217.7 


3 -4 


- 833.4 


+ 99.3 


- 1.6 


- 402.4 


- 56.4 


+ 


90.2 


4 -4 


- 294.8 


+ 40.7 


- 33.9 


- 250.5 


- 2.5 


+ 


14.8 


5 -4 


- 72.0 


+ 10.1 

m 


8.1 


- 66.4 


- 2.4 


+ 


0.9 


6 -4 


- 14.5 


+ 1.8 


1.8 


- 16.4 


0.5 






7 -4 


3.4 


+ 0.3 




- 2.9 








-2 -5 


1.6 




• 


+ 1.7 









16 



h «' 


«i 


Vi 


1 


COB 


Bin 


cos 


sin 


cos 


sin ' 


-1 -6 


.« 


10.1 


+ 


1.9 


+ 


2.1 


+ 10.4 


- 2.1 


+ 0.2 


-5 


— 


47.7 


+ 


7.9 


+ 


4.1 


+ 46.9 


+ 1.8 


+ 1.3 


1 -5 


— 


222.1 


— 


13.4 


— 


15.2 


+ 218.3 


- 11.5 


+ 10.6 


2 -5 


— 


148.9 


+ 


21.4 


+ 


52.2 


+ 188.6 


+ 13.8 


9.1 


3 -6 


+ 


204.2 


— 


30.9 


— 


40.0 


+ 7.4 


+ 20.9 


- 39.4 


4 -6 


+ 


20.8 


+ 


7.2 


+ 


20.2 


+ 113.3 


5.5 


+ 8.6 


5 -5 


+ 


2.5 


+ 


2.9 


+ 


1.1 


+ 20.6 


+ 0.6 


+ 2.6 


6 -5 


+ 


3.1 


~ 


0.5 


+ 


0.5 


+ 6.1 


- 0.5 




7 -6 


+ 


1.7 










+ 2.4 


. 




8 -5 


+ 


0.9 










■¥ 0.9 






-2 -6 


+ 


0.7 


+ 


0.3 


+ 


0.2 


- 0.7 






-1 -€ 


+ 


1.3 


— 


2.8 


— 


4.2 


1.9 


+ 1.2 




-6 


+ 


14.0 


— 


2.3 


+ 


2.1 


- 14.4 


4.0 


- 0.3 


1 -6 


+ 


191.1 


+ 


lii.o 


+ 126.8 


- 187.8 


1.4 


- 2.7 


2 -6 


+ 


166.8 


+ 


64.2 


— 


62.6 


— 66.6 


+ 2.7 


- 2.6 


3 -6 


— 


153.2 


— 


78.5 


+ 


•95.3 


- 77.5 


- 14.6 


+ 22.4 


4 -6 


— 


37.1 


— 


32.5 


+ 


11.8 


- 87.9 


+ 1-6 


5.5 


5 -6 


— 


25.6 


— 


3.1 


+ 


11.6 


1.8 


- 1.7 


+ 2.6 


6 -6 


— 


9.0 


— 


0.3 


+ 


1.9 


- 2.2 




+ 0.9 


7 -6 


— 


2Ji 






+ 


0.9 








-3 -7 


_ 


OS 


+ 


0.5 


_ 


0.2 


+ 0.4 


• 




-2 -7 


— 


M 


+ 


4.3 


+ 


4.3 


+ 2.1 






-1 -7 


— 


9.4 


+ 


16.8 


+ 


15.9 


+ 9.2 


1.9 




-7 


— 


41.5 


+ 


57.1 


+ 


54.6 


+ 41.9 


5.3 


- 0.5 


1 -7 


— 


237.0 


+ 


146.4 


+ 103.9 


+ 234.6 


- 83.3 


- 5.1 


2 -7 


+ 


162^ 


— 


86.7 


+ 110.3 


- 238.0 


+ 29.9 


4.7 


3 -7 


+ 


290.3 


— 


153.9 


+ 137.5 


+ 272.2 


8.9 


+ 17.8 


4 -7 


.— 


20.6 


— 


30.8 


+ 


37.4 


0.0 


2.5 


+ 4.9 


5 -7 


— 


2.3 


— 


11.4 


+ 


4.1 


- 17.7 


+ 0.3 


1.6 


6 -7 


— 


,5.4 


- 


1.0 


+ 


4.1 


+ 0.6 


0.4 


+ 0.7 


7 -7 


— 


HA 


— 


0.3 


+ 


1.3 


- 0.3 






-1 -8 


.^ 


1.6 


.. 


1.4 


_ 


1.4 


+ 1.7 






-« 


— 


5.8 


— 


8.3 


• 


8.4 


+ 6.1 


- 0.6 




1 -« 


_ 


16.8 


— 


21.4 




22.0 


+ 18.8 


+ 15.6 


" 1.0 


2 -« 


+ 


46.1 


+ 


43.3 


+ 


39.6 


- 43.5 


+ 1.4 


- 0.7 


3 -8 


+ 


44.0 


+ 


50.4 


— 


46.7 


+ 39.6 


4.0 


+ 0.9 


4 -8 


— 


12.4 


— 


11.7 


+ 


9.6 


- 14.1 


0.4 


0.4 


5 -8 


— 


7.7 


— 


3J) 


+ 


5.4 


2.0 


0.3 


+ 0.7 


6 -8 


+ 


0.6 


— 


2.2 


— 


0.1 


4.0 




- 0.5 


7 -8 


— 


0.9 


+ 


0.3 


+ 


0.6 


+ 0.8 










Normal Places reftrred to 


the Mean Equinox 18540. 


Berlin M. 1 


1 
• 


a 


9 


Berlin M. T. 


a 


d 






O 1 » 


O 1 It 




O 1 K 


O 1 « 


1852. July 


1.0 


271 35 16.53 


- 8 35 16.00 


1855, April 26.0 


223 23 31.65 


- 58 16.38 


1852, October 


1.0 


274 56 46.92 


-18 24 28.78 


1856, October 22.0 


39 13 48.02 


- 5 12 59.07 


1853, January 


1.0 


322 28 46.75 


-16 2 17.53 


1858, March 20.0 


182 4 41.86 


+ 7 34 3.35 


1854, January 


28.0 


128 3 16.18 


+12 2 48.34 


1859, July 8.0 


278 7 52.10 


- 9 19 9.96 



16 



$1 




Ci 




n 




+11421 


-15176 


-2756 


+14787 


-10133 


-6858 


+ 4084 


-19862 


-2823 


+ 9001 


-16524 


- 8192 


+ 1750 


-33592 


-2105 


+10510 


-30074 


-11002 


+39074 


-4084 


+3665 


+38902 


+ 6322 


+ 1899 


+ 2042 


- 2185 


+ 532 


+ 2592 


- 1580 


- 98 


+ 1754 


-14556 


- 380 


+ 5566 


-12885 


- 4268 


+ 5642 


-2660 


+2672 


+ 6360 


- 1575 


+ 1788 


+ 8584 


-10494 


-4500 


+10653 


- 6160 


- 7252 



For fi, i7n Ci, the plane of the orbit of Melpomene is the fundamental plane, but {, fjy {; are referred to the 
equator. The transformation is effected by means of the formulas on pages 391 and 392. 
We derive firom w' = 16M6' 53".3, Q' = 19M6' 43".7, and i' = 15^ 28' 17".2 for 1854.0 : — 



cos (a?! x) 
cos (yi x) 
cos (zi x) 



+ 0.959273 
— 0.268411 
4- 0.088074 



cos (xi y) = + 0.282146 
cos (y, y) = 4- 0.925742 ^ 
cos {zi y) = — 0.251799 ' 



cos (Xi z) 
COS (yi z) 
cos {zy z) 



— 0.018949 
+ 0.266394 
+ 0.963765 



The computation of the normal places &om the osculating elements for 1854.0 with the perturbations {, 17, & 
gives the following equations of condition for the determination of the corrections of the elements : — 



+1.72507 


-3.46371 


+1.76341 


-0.01327 


+0.11791 


- 9.60585 


+ 157.29^ 


+1.05428 


-2.12179. 


+0.96271 


-0.00356 


-H).03244 


- 5.53250 


+ 26.24 


+0.98888 


-1.13494 


+0.69111 


-0.02955 


+0.01693 


- 3.91254 


- 184.68 


+1.54040 


+3.09070 


+1.69341 


-0.05026 


-0.05610 


+ 0.38965 


- 508.67 


+1.05335 


-1.21848 


+1.51267 


-0.04736 


+0.35622 


+ 5.19856 


+ 75.05 


+3.21295 


+1.63979 


+2.06075 


-0.07675 


+0.47456 


+33.30130 


-1902.90 


+1.01318 


+0.73413 


+1.50797 


-0.08393 


+0.19514 


+15.62610 


- 219.44 


+1.85143 


-3.64800 


+1.80356 


-0.01777 


+0.07135 


+37.14650 


- 606.95 




dM 


^9 dn 




«8 


^t 100 « 


^ 


-0.08528 


+0.22198 


-0.13034 


+0.17877 


+1.44227 


+ 0.73639 


- 87.12 


-0.12241 


+0.18470 


-0.09555 


+0.17529 


+0.48963 


+ 0.52905 


- 26.89 


+0.12166 


-0.18671 


+0.08963 


+0.12534 


-0.11444 


- 0.53821 


- 35.08 


-0.11837 


-0.24087 


-0.14720 


-0.27302 


-0.64995 


- 0.13495 


+ 82.14 


-0.25846 


+0.20020 


-0.38766 


-0.08737 


+1.41267 


- 1.07558 ' 


- 23.25 


+0.92431 


-0.01619 


+0.57207 


+0.16001 


-1.80113 


+ 9.04078 


- 511.75 


-0.27122 


-0.25501 


-0.39779 


-0.21930 


• +0.73969 


- 4.07944 


+ 93.35 


-0.04169 


+0.15224 


-0.08194 


+0.20950 


+1.35572 


- 0.58380 


- 67.39. 



= 



From which, by the method of least squaresi is obtained : — 

d M— -1-12' 16".46 ^9 = 4-1' 33".89 ^ » = — 9' 0:'.57 

J I =4-0' 12".08 ^ /* = + 0".15125 

and thus finally the pure elliptical elements : — 

1854, Jan. 0, Washington Mean Time. 

M— %^ i 53.31 
ff = 15 5 30.95 

8 = 150 3 49.70 
t = 10 9 16.85 

9 = 12 34 20.18 
/4 = 1020".11977 

log a = 0.3609032 



^ a = + 2' 41".49 



M. Eq. Ep. 



o # w 

«' = 16 7 48.6 
a' = 19 16 5.9 
t' = 15 27 48.0 



17 

With these elements, and the aboTO perturbations^ I have constructed tables which represent the normals as 
follows : — 



a cos d 


/Id 


Ja COS d 


jd 


+L8 


-1.5 


-Jsi ' 


+1.2 


—3.6 


—4.3 


+8.8 


—0.3 


—2.0 


—1.3 


+5.5 


—4.9 


—1.3 


—2.3 


—0.6 

• 


+1.4 



This result is certainly satisfactory, since the perturbations by Saturn have been neglected. 

For curiosity's sake I have computed an approximation of the secular variations of the elements from the 
terms multiplied by t They are : — 



n = + 82".0l1 
8 =-35.01 [, 
i =— 0.33 / 
9=4- 0.68 J 



Jn = 

ji' =— o.^a /in one year. 



II. ON THE CONSTRUCTION OF THE TABLES OF MELPOMENE. 



13EF0SE entering into the details of the construction of the tables, I would take the libertj pf making some 
^^ general remarks on the treatment of asteroids at the present time. 

After two oppositions it is possible to determine the elements of an asteroid near enough the truth for 
computing the perturbations, and I think those bj Jupiter are sufficient for our present purposes. Three 
oppositions, then, admit the more accurate determination of the elements, and after about eight oppositions 
thej can be finallj corrected for the computation of the general perturbations of the first order by Jupiter. 
Preliminary tables constructed upon them will give, for the next fifty years, the ephemeris near enough to find 
the planet, and for forming normal places. Aft^r that, a computer can do something definite ; then he may 
compute the perturbations of the second order by using those known of the first order, or he may find it 
necessary to recompute the first order with the elements upon which the preliminary tables are based. And 
only then it will be necessary to calculate the perturbations by Saturn also. Our duty in our time with re- 
spect to the asteroids is, to avoid all superfluous work on them, and to get out as soon as possible such prefim- 
inary tables. Those asteroids which are of special interest, as, for instance, Leucothea and Euphrosyne for the 
determination of the mass of Jupiter, must of course be treated in a different manner. For those it will be 
best to carry on the special perturbations by Saturn, Jupiter, Mars, Earth, and Venus for a number of years. 

A number of small terms and equations have been omitted, since six decimal places were found to be suffi- 
cient in the tables. If we denote the Arguments in the following manner, 



I — ^ 


M' 


XVI — - 


- M—SM* 


XXXI — 


bM AM' 


11 = 


M M' 


XVII — 


4Jf 3M' 


XXXII — 


3 M^ 8 M' 


m — 


M BM' 


XVIII — 


5M 2M' 


XXXIII — 


— 4Jf— if' 


IV — 


M 2M' 


XTX = 


3M 1 M' 


XXXIV — 


1 M 2M' 


V — 


2M SM' 


x\ — 


^M SJf' 


:jlxxv — 


5 M— 6 M' 


VI — 


SM 2M' 


XXI — - 


-2M—ZM' 


XXXVI — 


QM M' 


VII — 


2M M' 


^K.n — 


M IM' 


X3:xvn — 


4 M— b M' 


VIII — - 


M 2M' 


xxm — 


M 5 M' 


xxxvin — 


AM 1 M' 


IX ^- 


M M' 


XXIV — 


3M 5M' 


XXXIX — 


M SM' 


>: — 


M—4:AP 


XXV — - 


- 8 M— 2 M' 


XL — 


1 M 3M' 


XI — 


M 


ILXVI — 


M (jM' 


XLI — . 


— M—bM' 


XII = 


SM— M' 


XXVII — 


2M—1M' 


XLII — ■ 


— M—IM' 


XIII — 


SM—4M' 


XXVIII — 


2M 5M' 


XLIII — 


M ' AM' 


XIV — - 


2M M' 


>:xTX = - 


3M M' 


XLIV — 


b M—SM' 


XV — 


^M— M' 


XXX — 


bM W 


XLV = 


b Jf — 7 M' 



the perturbations are : — 



19 



• 


1 

COS 


1 


»/i 




ii 




sin 


cos 


•in 


008 


sin 1 


OM 


- 84.94< 




-1022.41f 


• 


+ 


146.67/ 






M 


- 4.74< 


+4279.97^ 


-4154.40^ 


- 11.92/ 


— 


448.23/ 


+ 493.85/ 1 


2Af 


+ 25.6» 


+1241.89^ 


-1226.46^ 


i- 24.98/ 


— 


48.01/ 


+ 


53.12/ 


ZM 


+ 8.30e 


+ 325.86^ 


- 322.92^ 


+ 8.27/ 


- 


7.72/ 


+ 


8.56/ 


AM 


+ 2.50« 


+ 66.21^ 


- 85.92^ 


+ 2.37/ 


— 


147/ 


+ 


1.63/ 


bM 


+ 0.68< 


-h 22.98< 


- 22.70e 




— 


0.31/ 


+ 


0.34/ 


63f 


+ 0.1« 


+ 6.19< 


- 6.02^ 




— 


0.07/ 


+ 


0.08/ 


TM 




+ 1.3K 


- 1.37/ 












I 


+ 7732.7 


- 671.7 


- 325.3 


- 7809.7 


+ 


428.1 


__ 


312.4 


21 


--19149.5 


+ 2127.3 


+ 2083.7 


+19003.2 


- 


428.6 


+ 


600.3 


31 


+ 5724.9 


+ 4.2 


- 15.3 


- 5630.2 


+ 


187.9 


— 


208.4 


41 


+ 1.4 


- 12.1 


- 22.6 


4.0 


+ 


27.9 


— 


21.9 


51 


- 47.7 


+ 7.9 


+ 4.1 


+ 46.9 


+ 


1.8 


+ 


1.3 


61 


+ 14.0 


2.3 


+ 2.1 


- 144 


— 


4.0 


— 


0.3 


71 


- 41.5 


+ 57.1 


+ 54.6 


+ 41.9 


— 


5.3 


— 


0.5 


81 


5.8 


8.3 


8.4 


+ 6.1 


- 


0.5 






U 


- 1340.7 


- 82.3 


0.9 


- 1289.8 


_ 


554.6 


+ 


231.6 


211 


+10930.4 


- 1159.0 


+ 1065.5 


+10367.5 


+ 


244.1 


— 


J 46.5 


3n 


~ 3779.0 


+ 539.8 


^ 523.1 


" 3638.3 


— 


694 


+ 


141.1 


4n 


- 294.8 


+ 40.7 


- 33.9 


- 250.5 


— 


2.5 


+ 


14.8 


511 

• 


+ 2.5 


+ 2.9 


+ 1.1 


+ 20.6 


+ 


0.6 


+ 


2.5 


611 


9.0 


0.3 


+ 1.9 


- 2.2 






+ 


0.9 


7n- 


2.4 


~ 0.3 


-1- 1.3 


0.3 

9 











ra 


+ 9598.9 


-2097.8 


- 1894.6 


- 9736.8 


+ 


145.1 


— 


261.1 


2 in 


+ 166.8 


+ 64.2 


- 62.6 


- 66.6 


+ 


2.7 


— 


2.5 


IV 


- 8330.7 


•f 1305.0 


+ 754.2 


+ 9254.2 


+ 


525.7 


^ 


787.6 


2 IV 


+ 748.2 


- 120.8 


- 111.6 


- 32.3 


- 


131.7 


+ 


217.7 


3 IV 


- 153.2 


- 78.5 


+ 95.3 


^ 77.5 


— 


14.6 


+ 


224 


4 IV 


- 12.4 


- 11.7 


+ 9.6 


- 14.1 


— 


04 


— 


04 


V 


- 6031.4 


- 17.9 


+ 509.0 


-^isms 


.m. 


842.5 


+ 


1273.3 


2V 


- 37.1 

• 


- 32.5 


+ 11.8 


- 87.9 


+ 


1^ 


- 


5.5 


VI 


+ 4932.9 


- 540.5 


+ 540.7 


+ 4849.2 


+ 


3.7 


.^ 


46.1 


2 VI 


- 14.5 


+ 1.8 


1.8 


- 16.4 










VU 


-3739.2 


+ 227.2 


- 192.7 


-3658.9 


^ 


202.1 


— 


114.3 


2 VII 


4- 1507.9 


- 166.7 


4- 166.1 


+ 1497.3 


+ 


1.5 


^ 


74 


3vn 


- 804 


+ 13.6 


- 9.6 


- 56.7 


— 


0.7 


+ 


0^ 


vni 


- 3513.0 


+ 213.1 


+ 218.7 


+ 3500.3 


— 


72.0 


+ 


85.4 


avin 


3.2 


+ \A 


+ 0.9 


+ 2.7 










IX 


+ 2208.5 


- 55.3 


- 72.4 


-21884 


+ 


226.2 


.^ 


236.6 


2 IX 


- 778.1 


+ 36.1 


+ 36.1 


+ 7794 


- 


9.2 


+ 


12.0 


SIX 


+ 65.9 


+ 3.6 


+ 3.5 


- 66.1 


+ 


0.6 


— 


0.7 


4TX 


1.1 






+ 1.1 










X 


+ 1826.7 


- 182.2 


- 135.1 


- 1854.9 


+ 


59.7 


— 


91.2 


2X 


+ 46.1 


+ 43.3 


+ 39.6 


- 43.5 


+ 


14 




0.7 



20 





«i 


Vi 




ii 


1 


cos 


sin 


cos 


sin 


cos 


sin 1 


OXT 


- 699.7 






+ 


75.5 


• 


_ 


202.6 






XI 


+ 1118.5 


— 


5.6 


— 


9.4 


+ 901.6 


+ 


129.9 


+ 


143.4 


2 XT 


+ 463.6 


— 


31.7 


+ 


28.9 


+ 433.4 


+ 


38.2 


+ 


42.2 


3 XT 


+ 100.7 


— 


15.4 


+ 


13.1 


+ 97.4 


+ 


5.2 


+ 


6.6 


4X1 


+ 23.3 


— 


5.2 


+ 


4.9 


+ 21.1 


+ 


0.8 


+ 


1.0 


6XJ 


+ 5.8 


— 


1.5 


+ 


1.7 


+ 6.1 










XU 


- 1092.5 


+ 


72.3 


— 


70.3 


- 1081.8 


^ 


22.9 


^ 


10.7 


2xn 


+ 122.5 


— 


13.7 


+ 


12.7 


+ 112.6 










XIII 


- 833.4 


+ 


99.3 


^ 


1.6 


- 402.4 


_ 


56.4 


+ 


90.2 


2X111 




— 


2.2 






- 4.0 










XIV 


+ 494.5 


+ 


26.8 


+ 


26.3 


- 491.7 


+ 


22.7 


_ 


26.9 


2XTV 


- 50.0 


+ 


1.9 


+ 


2.0 


+ 52.5 










XV 


- 300.6 


+ 


19.9 


_ 


19.6 


- 300.2 


^ 


4.2 


__ 


1.6 


2 XV 


+ 8.0 


— 


0.8 


+ 


0.9 


+ 7.7 










XVI 


+ 1128.7 


+ 


45.6 


+ 


42.7 


" 1120.9 


+ 


21.1 


_ 


22.1 


XVII 


- 1034.5 


+ 


161.6 


— 


156.4 


- 1022.7 


— 


18.6 


+ 


16.8 


xvm 


t- 428.2 


— 


47.6 


+ 


47.9 


+ 432.3 






— 


1.4 


XTX 


+ 290.3 


— 


153.9 


+ 


137.5 


+ 272.2 


— 


8.9 


+ 


17.8 


XX 


~ 268.1 


+ 


43.2 


— 


42.6 


- 269.3 


— 


3.7 


+ 


3.0 


XXI 


+ 245.3 


+ 


13.5 


+ 


13.2 


- 263.7 


+ 


3.3 


— 


3.6 


XXTT 


- 237.0 


+ 


146.4 


+ 


103.9 


+ 234.6 


— 


83.3 


— 


5.1 


XXTTT 


- 222.1 


— 


13.4 


— 


15.2 


+ 218.3 


— 


11.5 


+ 


10.6 


XXTV 


+ 204.2 


— 


30.9 


— 


40.0 


+ 7.4 


+ 


20.9 


— 


39.4 


XXV 


- 192.0 


+ 


7.5 


+ 


7.8 


+ 192.5 


— 


1.7 


+ 


2.1 


XXVI 


+ 191.1 


+ 


141.0 


+ 


126.8 


- 187.8 


— 


1.4 


— 


2.7 


XX vn 


+ 162.0 


^^ 


86.7 


+ 


110.3 


- 238.0 


+ 


29.9 


— 


4.7 


XXVFTT 


- 148.9 


-1- 


21.4 


+ 


52.2 


+ 188.6 


+ 


13.8 


— 


9.1 


XXIX 


+ 122.3 


+ 


11.8 


+ 


11.8 


- 122.9 


+ 


4.2 


— 


4.5 


XXX 


- 79.0 


+ 


5.0 


— 


5.4 


- 84.8 










XXXI 


- 72.0 


+ 


10.1 


— 


8.1 


- 66.4 


— 


2.4 


+ 


0.9 


xxxn 


+ 44.0 


-1- 


50.4 


— 


46.7 


+ 39.6 


— 


4.0 


+ 


0.9 


XXXIII 


+ 32.1 


+ 


3.7 


+ 


3.5 


- 32.4 


+ 


0.8 


— 


0.9 


XXXTV 


+ 30.7 


— 


3.5 


+ 


3.0 


+ 29.9 










XXXV 


- 25.6 


— 


3.1 


+ 


11.6 


- 1.8 


— 


1.7 


+ 


2.6 


XXXVI 


- 21.9 


+ 


1.3 


— 


1.1 


- 20.7 










xxxvn 


+ 20.8 


-1- 


7.2 


+ 


20.2 


+ 113.3 


— 


5.5 


+ 


8.6 


XXX vm 


- 20.6 


— 


30.8 


+ 


37.4 


0.0 


— 


2.5 


+ 


4.9 


XXXIX 


~ 16.8 


— 


21.4 


— 


22.0 


+ 18.8 


+ 


15.5 


— 


1.0 


TTTi 


- 17.7 


+ 


3.1 


— 


3.0 


- 17.2 










XLI 


- 10.1 


+ 


1.9 


+ 


2.1 


+ 10.4 


— 


2.1 


+ 


0.2 


XLH 


9.4 


+ 


16-8 


+ 


15.9 


+ 9.2 


— 


1.9 




0.0 


XLIII 


8.9 


+ 


1.2 


+ 


1.2 


+ 9.3 


+ 


4.3 


^"^ 


2.5 


XLIV 


7.7 


— 


3.0 


+ 


5.4 


2.0 










XLV 


2.3 


— 


11.4 


+ 


4.1 


- 17.7 




0.0 


— 


1.6 



Tables for the equation of the centre and the radius vector have been superseded by solving Kepler's 
problem in the manner I have shown in Vol. III. No. 53 of the Astronomical Journal^ viz. : — If we sup- 
pose one of the radii vectores to turn uniformlj about one of the foci, describing therefore the mean anomaly. 



21 

the other radius vector will then, in not very eccentric ellipses, describe nearly the true anomaly. This 
auziliaiy anomaly, denoting with v', we have, simply, 



• 1 g 

cot ^ t/ = . cot ^ J£ 



1 — e . 



The logarithm of the constant factor ytt is for Melpomene = 9.8078595, and log p = 0.3398226 for the 
computation of the radius rector by means of r = r— r- 

The correction c, to be added to v' in order to get the true anomaly v, is given in Table IT., with Jf as the 
argument For the construction of this table I had c developed in the following series : — 



_ P 

ecoBv 



<? = — 526.495 sin M 
+ 2232.957 sin 2 M 
+ 819.532 sin 3 Jfcf 
4- 245.033 sin 4 if 



e = 



+ 68.825 sin 5 if 
4- 18.848 sin 6 if 
4- 5.096 sin 7 if 
+ 1.395 sin 8 if 



c = 



+ 0.373 sin 9 if 
+ 0.103 sin 10 M 
+ 0.053 sin 11 if 



JShoamph for computing a Flac9 from the Tables. 
1861, Feb. 5'* 5»» 58* 15' Washington M. T. = Feb. 5*» 12»» BerUn M. T. 

We write down on a scrap of paper the constants tp be used. From Table V. the logarithms of 



loge 

9.337800 


9.807860 


log;> 
0.339823 


COB (Xl X) 

9.982068 


COB (yi x) 
9.427362» 


COB (Z\ X) 

8.943100 


cos (xi y) 
9.449004 


cos (yiy) 
9.966656 


COB {ziy) 

9.400622n 


COB {Xl Z) 

8.144356n 


cog (yi«) 
9.424948 


cos (Zi z) 

9.984015 



and from Table VI., 

A* 
105** 34' 42".6 



!&" 53' 23".8 



357** 0' 0".6 



log sin a 
9.998323 



log sin b 
9.985806 



log sin c 
9.425543 



Af=: mean anomaly, and t ^ time since 1854.0 are taken from Table L 



M 



1861, 84° 42 59.56 


+7.00068 




cot i if 


47 29 38.8 


9.962142 


Feb. 8 47 3.72 


0.08488 


1 — 
1 + 


- cot ^ if cot J t;' 


59 30 30.4 


9.770002 


5 days 1 25 0.60 


0.01369 


1/ 


119 1 0.8 




5 hours 3 32.53 


0.00057 




From Table TT. c — 


26 10.1 




58 minutes 41.09 






V 


118 34 50.7 




15 seconds 0.17 






cos V 

6 COS V 


—0.104133 


9.679789i» 


94 59 17.67 


+7.09982 


9.017589» 








1 + COS t? 


0.895867 


9.952243 








r 




0.387580 



22 



Formation of the Arguments from TcMe IH.* 





I. 


n. 


in. 


IV. 


V. 


VI. 


VII. 


VIIL 


IX 


1861, 


237.828 


322.545 


78.202 


200.37 


162.92 


9.81 


47.26 


30.94 


153.11 


Feb. 


357.425 


6.209 


1.058 


3.63 


9.85 


21.20 


14.99 


346.07 


348.64 


5 days 


359.584 


1.001 


0.171 


0.59 


1.59 


3.42 


2.42 


357.75 


358.17 


6 hours 


35J9.979 


0.050 


0.008 


0.03 


0.08 


0.17 


0.12 


359.89 


359.91 



234.816 



329.805 



79.439 



204.62 



174.44 



34.60 



64.79 



14.65 



139.83 







XI. 


XII. 


xra. 


XIV. 


XV. 


XVL 


XVll. 


xvm. 


1861, 


316.03 


84.72 


131.98 


125.46 


68.40 


216.7 


268.8 


332.4 


179.2 


Feb. 


358.48 


8.78 


23.78 


16.05 


339.85 


32.6 


343.5 


27.4 


38.8 


5 dajs 


359.76 


1.42 


3.84 


2.59 


356.75 


5.3 


357.3 


4.4 


6.3 


6 hoars 


359.99 


0.07 


0.19 


0.13 


359.84 


0.3 


359.9 


0.2 


0.3 



314.26 



94.99 



159.79 



144.23 



44.84 



254.9 



249.5 



4.4 



224.6 





XIX. 


XX. 


XXI. 


XXII- 


XXIU. 


XXIV. 


XXV. 


XXVI. 


XXVII. 


1861, 


118.9 


57.1 


184.1 


309.5 


193.9 


3.3 


221.5 


71.7 


34.2 


Feb. 


8.3 


36.2 


334.7 


350.8 


355.9 


13.5 


328.5 


353.3 


359.5 


5 days 


1.3 


5.8 


355.9 


358.5 


359.3 


2.2 


354.9 


358.9 


359.9 


6hoiirs 


0.1 


0.3 


359.8 


359.9 


0.0 


0.1 


359.8 


0.0 


0.0 



128.6 



99.4 



154.5 



298.7 



189.1 



19.1 



184.7 



63.9 



33.6 





XXVlll. 


XXIX. 


XXX. 


XXXI. 


XXXll. 


XXXIII. 


XXXIV. 


XXXV. 


XXX VL 


1861, 


278.6 


343.7 


301.4 


294.9 


356.8 


259.0 


348.7 


50.6 


26.1 


Feb. 


4.7 


331.1 


41.3 


33.6 


5.7 


322.3 


56.3 


28.5 


50.1 


5 days 


0.8 


355.3 


6.7 


5.4 


0.9 


353.9 


9.1 


4.6 


8.1 


6 hoars 


0.0 


359.8 


0.3 


0.3 


0.1 


359.7 


0.5 


0.2 


0.4 



284.1 



309.9 



349.7 



334.2 



3.5 



214.9 



54.6 



83.9 



84.7 





XXXV 11. 


XXXVllI. 


XXXI^L 


XL. 


XLI. 


XLn. 


XLin. 


XLIV. 


XLV 


1861, 


88.0 


203.7 


187 


226 


24 


140 


147 


166 


288 


Feb. 


22.3 


17.1 


348 


54 


338 


333 


341 


23 


26 


5 days 


3.6 


2.8 


358 


9 


. 357 


356 


357 


4 


4 


6 hoars 


0.2 


0.1 

























114.1 


223.7 


173 


289 


359 


109 


125 


193 


318 



With these Arguments the perturbations are computed from Table IV. 



* These Ailments being expressed in degrees and decimals, 360.0, 720i>, or 1080 0, most be sabiracted when one of the sums 
is greater than one of those nambers. 



23 





«i 


Vi 


(1 




• 




+ 


— 


+ 


— 


+ 


— 






Terms with t 


2608.5 




264.9 




502.0 




cos (xi r) h + 4820.0 




I 


1006.2 




2527.7 




95.0 




cos (yi x) 171 " 265.9 




n 


491.3 






397.8 




50.1 


cos (zi x) Ci + 49.0 




III 




43.5 




968.5 




21.9 


i + 4603.1 




IV 


753.4 






460.7 




8.8 






V 


497.6 






68.8 


96.4 




cos(jn^)^i + 1412.5 




VI 


375.1 




318.2 






2.3 


cos(yiy)i7i + 920.2 




vir 


■ 


240.2 




232.2 


- 


19.6 


COS (zi y) Ci - 140.4 




vm 




334.7 


109.8 






4.8 


^ + 2192.3 




IX 




185.2 




217.4 




33.9 




X 


136.1 




127.3 




10.8 




/ \ •• *v/v <v 




XI 




119.6 


79.7 






12.0 


COS [xi z) ii - 70.0 
oos.(yi z) iji + 264.3 
cos (zi z) Ci + 537.9 


t 


XII 


115.2 






37.1 


1.8 






xm 


73.6 






23.1 


9.9 








XIV 


37.1 






27.5 




0.3 


C + 732.2 


Redaction to the appar- 


XV 


5.1 




29.8 




0.3 




1 4/ 


ent equinox. 


XVI 




43.8 


104.2 




1.4 




siD (ii' + v) 224 9 33.3 9.843018. 


^ ^^ ^ 


xvn 




101.9 




23.5 




1.7 


r sin a 0.385903 


/+20.03 


xvm 

XIX 




27.2 

30.1 


12.7 


33.8 


0.1 
1.9 




X 0.228921, 


9 ,0.9765 
(7 338 24 


sin (B + v) 135 28 14.5 9.845888 


TTX 


8.7 






25.8 


0.3 




r sin h 0.373386 


sin ((r+ a') 111 9 9.9697 


XXI 

xxn 




21.7 
24.2 




12.3 
15.6 




0.5 
3.6 


y 0.219274 


tan df 9.3529 
+ 1.99 0.2991 


sin (a + v) 115 34 51.3 9.955195 


XXIII 


22.1 






2.0 


1.0 




r sin c 9.813123 


J a* +22.22 


XXIV 
XXV 


18.3 
19.1 






3.5 
2.5 


0.7 
0.1 




z 9.768318 


cos ( G + a) 9.5573^ 




XXVI 


21.2 






11.3 




0.3 


y +1.656815 


-i a' - 3.42 0.5338. 


xxvn 


8.7 






3.9 


2.2 




n + 2192 




XXVIU 




5.7 




17.0 


1.2 




Y -^.614699 




XXIX 


7.0 




10.2 




0.6 




^cos^'sina' +1.044306 0.018828 




XXX 
XXXI 




7.9 
6.9 


0.9 
2.0 


















0.3 


X -1.694031 
I + 4603 




XXXII 


4.6 






4.4 




0.4 




XXXTII 




2.8 


1.6 


^m^ m 






X +0.723955 




XXXIV 
XXXV 


1.5 


0.6 


2.6 


0.1 






JcoaSfcosa^ -^.965473 9.964740, 


f M 


Bin a' , M 9-865861 


XXXVI 




0.1 




2.1 






tan a' 132 45 13.3 0.034068. 


a = 132 45 35.5 


XXX vn 
xxxvni 


3.6 


0.2 


9.5 


2.7 


1.0 


0.1 






z +0.586568 


XXXIX 


1.5 




2.4 






1.5 


C + 732 




XL 




0.9 


1.5 








Z -0.266747 




XLI 




1.0 


0.2 






0.2 


J sin d' +0.320553 9.505900 




XLII 


1.9 




0.3 








J cos ()' 0.152967 




XLIII 


0.6 




0.7 






0.4 


cos a' ^ ^ ^ 9.989240 




XLIV 


0.8 






0.5 






tana^ +1242 5.8 9.352933 


a = +12 42 3.4 


XLV 


0.6 




1.5 


2614.1 


0.1 




J 0.163727 






6221.4 


1198.2 


3607.7 


720.8 


162.7 


^19 Vl9 il 


+ 5023.2 




+ 993.6 




+ 558.1 




a' and ^ are referred to the mean 




L 


3.700960 




2.997212 




2.746712 




eqninox 1861.0. 




M7 oompai 


tations foi 


r 1861, ^ 


inththeo 


scalatio 


ig elemen 


ts for 1854.0 aiid the special perturbations 1 


by Jupiter and Saturn, give 


for the same 1 


time: — 










» 132 4^33.3 














a s 














a» 


» + 12 42 2.0 














Ja 


2.2 














Jd 


1.4 





24 

Bj this close agreement between the two different computations, the correctness of the tables is sadsfactorilj 
proved. 

For the computation of an exact opposition ephemeris, it will be necessary only to compute the perturbations 
from 16 to 16 days fix)m the tables, and then to interpolate them twice in the middle, in order to get them 
from 4 to 4 days, with which interval such ephemerides are commonly calculated. For an approximate 
ephemeris for the whole year, the terms multiplied with the lime kid the first four equations will be sufii* 
cient, and also a direct computation of the perturbations only from 40 to 40 days, with afterwards two 
interpolations in the middle, if the ephemeris is to be computed from 10 to 10 days. 



25 



~ — 




TABLE I. 


» 






FOE THE MEAN ANOMALY. 






The times are referred to the meridian of Washington. 




Years. 


A£ 


t 


Years. 


3f 


t 




o i n 






f II 




1852 B 


233 17 25.88 


- 1.99863 


1877 


300 42 39.50 


+23.00068 


1853 


336 43 9.59 


- 0.99932 


1878 


44 8 23.22 


24.00000 


1854 


80 8 53.31 


0.00000 


1879 


147 34 6.93 


24.99932 


1855 


183 34 37.03 


+ 0.99932 


1880 B 


251 16 50.77 


26.00137 


1856^ 


287 17 20.86 


2.00137 


1881 


354 42 34.48 


27.00068 


1857 


30 43 4.58 


3.00068 


1882 


98 8 18.20 


28.00000 


1858 


134 8 48.29 


4.00000 


1883 


201 34 1.92 


28.99932 


1859 


237 34 32.01 


4.99932 


1884 B 


305 16 45.75 


30.00137 


1860 B' 


341 17 15.85 


6.00137 


1885 


48 42 29.47 


31.00068 


1861 


84 42 59.56 


7.00068 


1886 


152 8 13.18 


32.00000 


1862 


188 8 43.28 


8.00000 


1887 


255 33 56.90 


32.99932 


1863 


291 34 26.99 


8.99932 


1888 B 


359 16 40.74 


34.00137 ! 


1864 B 


35 17 10.83 


10.00137 


1889 


102 42 24.45 . 


35.00C68 


1865 


138 42 54.55 


11.00068 


1890 


236 8 8.17 


36.00000 

1 


1866 


242 8 38.26 


12.00000 


1891 


309 33 51.88 


36.99932 


1867 


345 34 21.98 


12.99932 


1892 B 


53 16 35.72 


38.00137 


1868 B 


89 17 5.81 


14.00137 


1893 


156 42 19.44 


39.00068 


1869 


192 42 49.53 


15.00068 


1894 


260 8 3.15 


40.00000 


1870 


296 S 33.25 


16.00000 


1895 


3 33 46.87 


40.99932 


1871 


39 34 16.96 


16.99932 


1896 B 


107 16 30.70 


42.00137 


1872 B 


143 17 0.80 


18.00137 


1897 


210 42 14.42 


43.00068 


1873 


246 42 44.51 


19.00068 


1896 


314 7 58.14 


44.00000 


1874 


350 8 28.23 


20.00000 


1899 


57 33 41.85 


44.99932 


1875 


93 34 11.95 


20.99932 


1900 B 


161 16 25.69 


' +46.00137 


1876 B 


197 16 55.78 


+22.00137 








Months. 


M 


t 


Days. 


M 


t 


January 


O 1 u 

0.00 


+0.00000 


1 


o 1 n 
17 0.12 


+0.00274 


February 


8 47 3.72 


0.08488 


2 


34 0.24 


0.00548 


March 


16 43 7.08 


0.16154 


3 


51 0.36 


0.00821 


April 


25 30 10.78 


0.24642 


4 


1 8 0.48 


0.01095 


May 


34 14.38 


0.32856 


5 


1 25 0.60 


0.01369 


June 


42 47 18.10 


0.41344 


6 


1 42 0.72 


0.01643 


July 


51 17 21.68 


0.49558 


7 


1 59 0.84 


0.01917 


August 


60 4 25.40. 


0.58046 


8 


2 16 0.96 


O.0219O 


September 


68 51 29.12 


0.66534 


9 


2 33 1.08 


0.C2464 


October 


77 21 32.72 


0.74748 


10 


2 50 1.20 


0.02738 


November 


86 8 36.44 


0.83236 


23 


5 40 2.40 


0.C5476 


December 


94 38 40.04 


+0.91450 


30 


8 30 3.60 


+0.06214 


m 


In Bissextile Years on 


e day must be subtracted from the date in the first two mont 

* 
• 


1 
t 

hs. 

1 

1 
1 



26 • 



• 




TABLE I.— Concluded. 

FOR THE MEAN ANOMALY. 






The times are referred to the meridian of Washington. 




1 

Hours. 


M 


t 


Hours. 


M 


t 


1 


1 H 

42.51 


+0.00011 


13 


9 12.57 


+0.00149 


2 


1 25.01 


0.00023 


14 


9 55.07 


0.00160 


3 


2 7.52 


0.00034 


15 


10 37.58 


0.00172 


1 4 


2 50.02 


0.00046 


16 


11 20.08 


0.00183 


5- 


3 32.53 


0.00057 


17 


12 2.59 


0.00195 


6 


4 15.03 


0.00069 


18 


12 45.09 


0.00206 


7 


4 57.54 


0.00080 


19 


13 27.60 


0.00218 


8 


5 40.04 


0.00092 


20 


14 10.10 


0.00229 


9 


6 22.55 


0.00103 


21 


14 52.61 


0.00241 


10 


7 5.05 


0.00114 


22 


15 35.11 


0.00252 


11 


7 47U56 


0.00126 


23 


16 17.62 


0.00264 


12 


8 30.06 


+0.00137 1 24 


17 0.12 


+0.00275 




M 


* 


1 


For Minutes. 


For Seconds. 


For Minutes. 


For Seconds. 


1 


o''.71 


M 

0.01 


31 


2h96 


II 
0.36 


2 


1.42 


0.02 


32 


22.67 


0.37 


3 


2.13 


0.03 


33 


23.38 


0.39 


4 


2.83 


0.05 


34 


24.09 


0.40 


5 


3.54 


0.06 


35 


24.80 


0.41 


6 


4.25 


0.07 


36 


25.50 


0.42 


7 


4.96 


0.08 


37 


26.21 


0.44 


8 


5.67 


0.09 


38 


26.92 


0.45 


9 


6.38 


0.11 


39 


27.63 


0.46 


10 


7.08 


0.12 


40 


28.34 


0.47 


11 


7.79 


0.13 


41 


29.05 


0.48 


12 


8.50 


0.14 


42 


29.76 


0.50 


13 


9.21 


0.15 


43 


30.47 


0.51 


14 


9.91 


0.16 


44 


31.17 


0.52 


15 


10.62 


0.17 


45 


31.88 


0.53 


16 


11.33 


0.19 


46 


32.59 


0.54 


17 


12.04 


0.20 


47 


33.29 


0.55 


18 


12.75 


0.21 


48 


34.00 


0.57 


19 


13.46 


0.22 


49 


34.71 


0.58 


20 


14.17 


0.23 


50 


35.42 


0.59 


21 


14.88 


0.25 


61 


36.12 


0.60 


22 


15.58 


0.26 


52 


36.83 


0.61 


23 


16.29 


0.27 


53 


37.54 


0.62 


24 


17.00 


0.28 


54 


38.25 


0.64 


25 


17.71 


0.29 


55 


38.96 


0.65 


26 


18.42 


0.31 


56 


39.67 


0.66 


27 


19.13 


0.32 


57 


40.38 


0.67 


28 


19.84 


0.33 


58 


41.09 


0.68 


29 


20.54 


0.34 


59 


41.80 


0.70 


30 


21.25 


0.35 


60 


42.51 


0.71 


1 









27 



TABLE II. 

FOB THE CORRECTION <? TO BE ADDED TO THE AUXILIARY ANOMALY v*. 
Argument » M. For if > 180^ the Axgmneat is 360^ — M, «nd the aign of c to be reTerved. 



Aig. 



o 
0.0 

.5 
1.0 

^ 
2.0 

.5 
3.0 

.5 
4.0 

.5 

5.0 

.5 
6.0 

.5 
7.0 

.5 
8.0 

.5 
9.0 

.5 

10.0 

.5 
11.0 

.5 
12.0 

.5 
13.0 

.5 
14.0 

.5 

15.0 

.5 
16.0 

.5 
17.0 

.5 
18.0 

.5 
19.0 

.5 

20.0 
.5 

21.0 
.5 

22.0 
.5 



I N 

0.00 
+ 1 8.81 

2 17.58 

3 26.26 

4 34.79 

5 43.14 

6 51.27 

7 59.10 
9 6.61 

10 13.75 

+11 20.47 

12 26.74 

13 32.50 

14 37.71 

15 42.33 

16 46.31 

17 49.61 

18 52.20 

19 54.04 

20 55.08 

+21 55.28 

22 54.61 

23 53.03 

24 50.51 

25 47.02 

26 42.51 

27 36.96 

28 30.33 

29 22.60 

30 13.73 

+31 3.70 

31 52.48 

32 40.04 

33 26.36 

34 11.42 

34 55.19 

35 37.66 

36 18.80 

36 58.60 

37 37.03 

+38 14.08 

38 49.75 

39 24.01 

39 56.85 

40 28.27 
+40 58.26 



Diff. 



+48.81 
88.77 
66.88 
88.68 
68.SA 
86.13 
67.83 
87.61 
67. U 

66.78 

+66.37 
66.78 
66.31 
64.63 
63.96 
63.80 
83.69 
81.84 
61*04 

60.30 

+60.83 
68.43 
67.48 
66.61 
66.40 
64.46 
63.87 
63.37 
61.13 

40.97 

+48.78 
47*66 
46*83 
46^)6 
43.77 
43.47 
41.14 
39.80 
38.43 

37-06 

+86.87 
34.36 
33.84 
31.43 

+39.09 



Arg, 



o 
22.5 

23.0 

.5 
24.0 

.5 
25.0 

.5 
26.0 

.5 
27.0 

.5 
28.0 

.5 
29.0 

.5 
30.0 

.5 
31.0 

.5 
32.0 

.5 
33.0 

.5 
34.0 

.5 
35.0 

.5 
36.0 

.5 
37.0 

.5 
38.0 

.5 
39.0 

.5 
40.0 

.5 
41.0 

.5 
42.0 

.5 
43.0 

.5 
44.0 

.5 
45.0 



+40 58.26 
41 26.80 

41 53.88 

42 19.51 

42 43.66 

43 6.35 
43 27.56 

43 47.30 

44 5.57 
44 22.37 

+44 37.69 

44 51.56 

45 3.96 
45 14.90 
45 24.40 
45 32.46 
45 39.07 
45 44.27 
45 48.04 
45 50.40 

+45 51.38 
45 50.97 
45 49.19 
45 46.05 
45 41.57 
45 35.76 
45 28.65 
45 20.23 
45 10.53 
44 59.58 

+44 47.39 
44 33.97 
44 19.35 
44 3.55 
43 46.58 
43 2848 
43 9.25 
42 4^93 
42 27.52 
42 5.07 

+41 41.58 
41 17.08 
40 51.60 
40 25.15 
39 57.76 

+39 29.45 



DUF. 



n 

+38.64 
37.08 
36*68 
34.16 
33.68 
31.31 
19*74 
18.37 
16.80 

16.33 

+13*87 
13.40 
10.94 
9.60 
8*06 
6*81 
6.30 

3.n 

3.36 

+ 0*96 

- 0-41 
1*78 
3*14 
4.48 

6.81 
7*11 
8.43 
9.70 
10.96 

19.19 

-13.43 
14.63 
16.80 
18.97 
18*10 
19.38 
30.33 
31.41 
33.46 

33.49 

-34.60 
36.48 
36.46 
37.39 

-38.31 



Arg. 



o 

45.0 

.5 
46.0 

.5 
47.0 

.5 
48.0 

.5 
49.0 

.5 

50.0 

.5 
51.0 

.5 
52.0 

.5 
53.0 

.5 
54.0 

.5 

55.0 

.5 
56.0 

.5 
57.0 

.5 
58.0 

.5 
59.0 

.5 

60.0 

.5 
61.0 

.5 
62.0 

.5 
63.0 

.5 
64.0 

.5 

65.0 
.5 

66.0 
.5 

67.0 
.5 



+39 2945 
39 0.24 
38 30.16 
37 59.23 
37 2748 
36 54.93 
36 21.61 
35 47.54 
35 12.75 
34 37.25 

+34 1.07 
33 24.25 
32 46.80 
32 8.74 
31 30.10 
30 50.90 
30 11.17 
29 30.93 
28 50.19 
28 8.99 

+27 27.36 
26 45.30 
26 2.84 
25 20.01 
24 36.82 
23 53.31 
23 948 
22 25.37 
21 40.99 
20 56.37 

+20 11.52 
19 26.47 
18 41.24 
17 55.84 
17 10.30 
16 24.63 
15 38.86 
14 53.01 
14 7.08 
13 21.11 

+12 35.10 

11 49.07 

11 3M 

10 17.05 

9 31.08 

+ 8 45.17 



Diff. 



M 

-39.31 
30*08 
30*08 
31*76 
33*66 
33*33 
34*07 
34*79 
36*60 

36*18 

-36*83 
37*46 
38*06 
38-64 
80*90 
38.73 
40*34 
40*74 
41*30 

41*63 

-43*06 
43*46 
43.88 
43*19 
43*61 
48.88 
44*11 
44.88 
44*63 

44*86 

-46.06 
46.33 
46.40 
46.64 
46.67 
46-77 
46.86 
46.98 
46.97 

46.01 

-48^)8 
48.03 
48*00 
46*97 

-46.91 



Arg. 



o 

67.6 
68.0 

.5 
69.0 

.5 
70.0 

.5 
71.0 

.5 
72.0 

.6 
73.0 

.5 
74.0 

.5 
75.0 

.5 
76.0 

.5 
77.0 

.5 

78.0 

.5 
79.0 

.5 
80.0 

.5 
81.0 

.5 
82.0 

.5 

83.0 

.5 
84.0 

.5 
85.0 

.5 
86.0 

.5 
87.0 

.5 

88.0 
.5 

89.0 
.5 

90.0 



+ 8 45.17 
7 59.33 
7 13.57 
6 27.90 
5 42.35 
4 56.93 
4 11.65 
3 26.53 
2 41.58 
1 56.82 

+ 1 12.25 
+ 27.90 

- 16.23 
1 0.13 

1 43.78 

2 27.17 

3 10.29 

3 53.12 

4 35.67 

5 17.91 

- 5 593i 

6 41.45 

7 22.73 

8 3*66 

8 44.24 

9 24.46 
10 4.31 

10 43.79 

11 22.88 

12 1.57 

-12 39.87 

13 17.76 

13 55*23 

14 32.29 

15 8.92 

15 45.11 

16 20.86 

16 56.17 

17 31.03 

18 5.43 

-18 39.37 

19 12*85 

19 45.85 

20 18.38 
20 5042 

-21 21.98 



Diff 



If 

-46*84 
46.76 
46*67 
46*66 

46*43 
46*38 
46*13 
44*96 
44*76 

44.67 

-44*86 
44*13 
48*00 
43*66 
43*30 
48*13 
43*83 
43*66 
43*34 

41*08 

-41.61 
41*96 
40*08 
40*66 
40*33 
38*86 
39*48 
89.09 
3S*69 

88.80 

-87.89 
87.47 
37*06 
3G4» 
36* 19 
36*76 
36*31 
34.86 
84.40 

33*94 

-33*48 
33^X) 
83*63 
83*04 

-81*66 



28 



TABLE II.— Cbncluded. 

FOR THE CORRECTION c TO BE ADDED TO THE AUXILIARY ANOMALY v'. 
Aliment « M. For Jif > 18U° the Aigument b 360° — M, and the sign of c to be rerersed. 



Arg. 

9o!o 

91.0 

.5 
92.0 

.5 
93.0 

.5 
94.0 

.5 

95.0 

.5 
96.0 

.5 
97.0 

.5 
98.0 

.5 
99.0 

.5 

100.0 

.5 
101.0 

.5 
102.0 

.5 
103.0 

.5 
104.0 

.5 

105.0 

.5 
106.0 

.5 
107.0 

.5 
106.0 

.5 
109.0 

.5 

110.0 
.5 

111.0 
.5 

112.0 
.5 



-21 21.98 

21 53.05 

22 23.63 

22 53.72 

23 23.31 

23 52.40 

24 20.98 

24 49.05 

25 16.62 

25 43.67 

-26 10.21 

26 36.24 

27 1.75 
27 26.74 

27 51.20 

28 15.14 

28 38.56 

29 1.45 

29 23.82 
23 45.66 

-30 6.98 

30 27.77 

30 48.03 

31 7.76 
31 26.97 

31 45.64 

32 3.79 
32 21.41 
32 38.50 

32 55.06 

-33 11.10 

33 26.61 
33 41.59 

33 56.05 

34 9.99 
34 23.40 
34 36.30 

34 48.68 

35 0.54 
35 11.88 

-35 22.71 
35 33.02 
35 42.82 

35 52.10 

36 0.88 
-36 9.15 



Diff. 



-81.07 
80.A8 
80.09 
30.'A9 
39*09 
38.38 
38.07 
37.57 
37>06 

96.64 

-3«.08 
36*51 
34*99 
34.46 
38.94 
33*43 
33.89 
33.87 
31.84 

31*83 

-90.79 
SO -36 
19.78 
19.31 
18.67 
18*15 
17.63 
17.09 
16.66 

16.04 

-16.61 
14.98 
14*46 
18.94 
18.41 
13.90 
13.88 
11.86 
11.84 

10-88 

-10.81 
9*80 
9.38 
8.78 

- 8.37 



Al^. 



112.5 
113.0 

.5 
114.0 

.5 
115.0 

.5 
116.0 

.5 
117.0 

•5 
118.0 

.5 
119.0 

.5 
120.0 

.5 
121.0 

.5 
122.0 

.5 
123.0 

.5 
124.0 

.5 
125.0 

.5 
126.0 

.5 
127.0 

.5 
128.0 

.5 
129.0 

.5 
130.0 

.5 
131.0 

.5 
132.0 

.5 
133.0 

.5 
134.0 

.5 
ia5.0 



-36 9.15 
36 16.91 
36 24.18 
36 30.94 
36 37.20 
36 42.97 
36 48.25 
36 53.03 

36 57.33 

37 1.14 

-37 4.46 
37 7.31 
37 9.67 
37 11.55 
37 12.97 
37 13.91 
37 14*38 
37 14.39 
37 13.93 
37 13.01 

-37 11.64 
37 9.81 
37 7.53 
37 4.81 
37 1.64 
36 58.04 
36 54.00 
36 49.53 
36 44.63 
36 39.31 

-36 33.57 
36 27.41 
36 20.83 
36 13.84 
36 6.44 
35 58.63 
35 50*41 
35 41.80 
35 32.79 
35 23.39 

-35 13.60 
35 3.43 
34 52.87 
34 41.94 
34 30.64 

-34 18.97 



Diff. 



- 7.76 
7.37 
6*76 
6 36 
6*77 
6*38 
4.78 
4*30 
8*81 

8*83 

- 3*86 
3*86 
1*88 
1.43 
0-94 
0.47 

- 0*01 
+ 0*40 

0-93 

1*87 

+ l.«8 
3.38 
3.73 
8.17 
8.60 
4.04 
4.47 
4*90 
6*83 

6.74 

+ 6.16 
6.68 
6.99 
7*40 
7.8I 
8.33 
8.61 
9.01 
9.40 

9*79 

+10.17 
10.66 
10*98 
11*30 

+11*67 



Al^. 



135.0 

.5 
136.0 

.5 
137.0 

.5 
138.0 

.5 
139.0 

.5 

140.0 

.5 
141.0 

.5 
142.0 

.5 
143.0 

.5 
144.0 

.5 

145.0 

m5 
146.0 

.5 
147.0 

.5 
148.0 

.6 
149.0 

.5 

150.0 

.5 
151.0 

.5 
152.0 

.5 
153.0 

.5 
154.0 

.5 

155.0 
.5 

156.0 
.5 

157.0 



I II 
-34 18.97 

34 6.94 

33 54.55 

33 41.80 

33 28.70 

33 15.25 

33 1.46 

32 47.32 

32 32.85 

32 18.04 

-32 2.90 
31 47.44 
31 31.65 
31 15.55 
30 59.13 
30 42.41 
30 25.37 
30 8.04 
29 50.41 
29 32.48 

-29 14.26 
28 55.75 
28 36.96 
28 17.89 
27 58.54 
27 38.93 
27 19.05 
26 58.91 
26 38.51 
26 17.86 

-25 56.96 
25 35.81 
25 14.41 
24 52.78 
24 30.92 
24 8.83 
23 46.51 
23 23.98 
23 1.23 
22 38.27 

-22 15.10 
21 51.72 
21 28.14 
21 4.36 
20 40.38 

-20 16.21 



Diff. 



« 

+13*08 
13*89 
13.76 
13*10 
18*46 
19.79 
14*14 
14*47 
14*81 

16*14 

+16*46 
16*79 
16*10 
16-43 
16.73 
17.04 
17*88 
17*63 
17*08 

18*33 

+18.61 
18*79 
19*07 
19*86 
19*61 
19*88 
90*14 
30*40 
90*66 

90*90 

+31*16 
31*40 
31.68 
31.86 
93.00 
93.83 
93.63 
93.76 
93*96 

38*17 

+38*38 
38*68 
38*78 
38*98 

+34*17 



Arg. 

157°.5 
158.0 

.5 
159.0 

.5 
160.0 

.5 
161.0 

.5 
162.0 

.5 

163.0 

.5 
164.0 

.5 
165.0 

.5 
166.0 

.5 
167.0 

.5 

168.0 

.5 
169.0 

.5 
170.0 

.5 
171.0 

.5 
172.0 

.5 
173.0 

.5 
174.0 

.5 
175.0 

.5 
176.0 

.5 
177.0 

.5 
178.0 

.5 
179.0 

.5 
180.0 



20 16.21 
19 51.85 
19 27.32 
19 2.61 
18 37.73 
18 12.68 
17 47.47 
17 22.10 
16 56.58 
16 30.90 

-16 5.08 
15 39.11 
15 13.00 
14 46.76 
14 20.38 
13 53.88 
13 27.25 
13 0.51 
12 3.3.65 
12 6.68 

-11 39.61 

11 12.43 

10 45.15 

10 17.78 

9 50.32 

9 22.77 

8 55.14 

8 27.43 

7 59.64 

7 31.79 



7 
6 
6 
5 
5 
4 
4 
3 



3.87 
35.89 
7*85 
39.76 
11.62 
43.44 
15.21 
46.94 
3 18.65 
2 50.32 



- 2 21.07 
1 53.60 
1 25.21 
56.81 

- 28.41 
0.00 



Diff 



M 

+34.86 
34.68 
94.71 

94*88 
96*06 
96.31 
36.87 
96.69 
96*68 

96.89 

+36*97 
96.11 
96*94 
96.88 
36.60 
96.68 
96.74 
36*86 
36*97 

37*07 

+37*18 
37*38 
97*87 
37*46 
37*66 
37*68 
37*71 
37*79 
37*66 

37*93 

+37*98 
38*04 
38*00 
38.14 
38*18 
38*93 
38*37 
38*39 
38*38 

3S*36 

+36*87 
38*89 
38*40 
98*40 

+98*41 



^ 



29 











TABLE III. 
















FOB 


. THE ARGUMENTS. 








- 


A. 


For the difFerent Years. 


The times are referred to the meridian of Washington. 




Years. 


I. 


XL 


111. 


IV. 


V. 


VL 


VII. 


VIII. 


IX. 


1852 B 


150°924 


24'!214 


326^.061 


175°.14 


199''.35 


281°72 


257°.50 


68^56 


277.63 


1853 


120.598 


97.317 


338.513 


217.92 


315.23 


171.35 


74.04 


26448 


143.88 


1854 


90.273 


170.420 


350.966 


260.69 


71.11 


60.99 


. 250.57 


100.40 


10.12 


1855 


59.947 


243.524 


3.418 


303.47 


187.00 


310.63 


67.10 


296.32 


236.37 


1856 B 


29.539 


316.828 


15.905 


346.37 


303.19 


200.94 


244.12 


131.79 


102.25 


1857 


359.213 


29.931 


28.357 


29.14 


59.07 


90.58 


60.65 


327.71 


328.50 


1858 


32ft.888 


103.035 


40.810 


71.92 


174.96 


340.22 


237.18 


163.63 


194.74 


1859 


298.562 


176.138 


53.263 


114.70 


290.84 


229.85 


53.71 


359.55 


60.99 


1860 B 


268.154 


249.442 


65.749 


157.59 


47.04 


120.17 


230.73 


195.02 


286.87 


1861 


237.828 


322.545 


78.202 


200.37 


162.92 


9.81 


47.26 


30.94 


153.11 


1862 


207.503 


35.648 


90.654 


243.15 


278.60 


259.44 


223.79 


226.86 


19.36 


1863 


177.178 


108.752 


103.108 


285.93 


34.68 


149.08 


40.33 


62.78 


245.60 


1864 B 


146.769 


182.056 


115.594 


328.82 


150.88 


39.40 


217.34 


258.25 


111.48 


1865 


116.444 


255.159 


128.047 


11.60 


266.76 


289.03 


33.87 


94.17 


337.73 


1866 


86.119 


328.263 


140.500 


54.38 


22.64 


178.67 


210.41 


290.09 


203.97 


1867 


55.793 


41.366 


152.953 


97.16 


138.53 


68.30 


26.94 


126.01 


70.22 


1868 B 


25.385 


114.670 


165.440 


140.05 


254.72 


318.62 


203.95 


321.48 


296.10 


1869 


355.060 


197.774 


177.893 


182.83 


10.62 


208.26 


20.49 


157.41 


162.35 


1870 


324.734 


260.877 


190.346 


225.61 


126.49 


97.90 


197.02 


353.33 


28.59 


1871 


294.409 


333.981 


202.799 


268.39 


242.37 


347.53 


13.55 


189.25 


254.84 


1872 B 


264.001 


47.284 


215.286 


311.29 


356.57 


237.85 


190.57 


24.72 


120.72 


1873 


233.676 


120.388 


227.740 


354.06 


114.45 


127.49 


7.10 


220.64 


346.96 


1874 


203.350 


193.492 


240.192 


36.84 


230.33 


17.12 


183.63 


56.56 


213.21 


1875 


173.025 


266.595 


252.646 


79.62 


346.22 


266.76 


0.17 


252.48 


79.46 


1876 B 


142.617 


339.899 


265.134 


122.52 


102.42 


157.08 


177.18 


87.95 


305.34 


1877 


112.292 


53.003 


277.586 


165.29 


218.30 


46.72 


353.71 


283.67 


171.58 


1878 


81.967 


126.107 


290.040 


208,07 


334.18 


296.35 


170.25 


119.80 


37.84 


1879 


51.642 


199J310 


302.494 


250.85 


90.06 


185.99 


346.78 


315.71 


264.07 


1880 B 


21.234 


272.514 


314.981 


293.74 


206.26 


76.30 


163.80 


151.19 


129.95 


1881 


350.908 


345.618 


327.434 


336.53 


322.14 


325.95 


340.33 


347.11 


356.20 


1882 


320.583 


58.721 


339.887 


19.30 


78.02 


215.58 


156.86 


183.03 


222.44 


1883 


290.258 


131.825 


352.340 


62.08 


193.91 


105.22 


333.39 


18.95 


88.69 


1884 B 


259.849 


205.129 


4.827 


104.96 


310.11 


355.54 


150.41 


214.42 


314.57 


1885 


229.524 


278.232 


17.280 


147.76 


65.99 


245.17 


326.94 


50.34 


180.82 


1886 


199.198 


351.335 


29.732 


190.53 


181.87 


134.81 


143.47 


246.26 


47.06 


1887 


168.873 


64.439 


42.185 


233.31 


297.75 


24.44 


320.00 


82.18 


273.31 


1888 B 


138.465 


137.743 


54.672 


276.21 


53.95 


274.76 


137.02 


277.65 


139.19 


1889 


108.139 


210.846 


67.125 


318.98 


169.83 


164.40 


313.55 


113.58 


5.43 


1890 


77.814 


283.950 


79.578 


1.76 


285.71 


54.03 


130.09 


309.49 


231.68 


1891 


47.489 


357.053 


92.031 


44.54 


41.59 


303.67 


306.62 


145.41 


97.92 


1892 B 


17.080 


70.357 


104.517 


87.44 


157.79 


193.99 


123.63 


340.88 


323.80 


1^93 


346.755 


143.460 


116.970 


130.23 


273.68 


83.63 


300.17 


176.81 


190.05 


1894 


316.430 


216.564 


129.423 


172.99 


29.56 


333.26 


116.70 


12.r3 


56.30 


1895 


286.104 


289.667 


141.876 


215.77 


145.44 


222.90 


293.23 


208.65 


282.54 


1896 B 


255.696 


2.971 


154.363 


258.67 


261.64 


113.22 


110;25 


44.12 


148.42 


1897 


225.371 


76.075 


166.816 


301.49 


17.52 


' 2.85 


286.78 


240.04 


14.67 


1898 


195.045 


149.178 


179.268 


%44.22 


133.30 


252.49 


103.31 


75.96 


240.91 


1899 


164.720 


222.232 


191.721 


27.00 


249.28 


142.12 


279.84 


271.88 


107.16 


1900 B 


134.311 


295.5a5 


204.208 


69.90 


5.48 


32.44 


96.86 


107.35 


333.04 



30 



TABLE III.— (hntinued. 

FOR THE ARGUMENTS. 
Aft For tbe different Yews. The timet are referred to tbo meridian of WaahiBgton. 



Tears. 



[852 £ 

1853' 

[854 

1855 

1856^ 

L857 

1858 

L859 

[860 B 

1861 

1862 

1863 

L864 B 

1865 

1866 

1867 

1868 B 

1869 

1870 

1871 

1872 B 

L873 

1874 

1875 

1876 B 

1877 

1878 

1879 

1880 B 

1881 

1882 

[883 

[884 B 

[885 

[886 

[887 

[888 B 

[889 

[890 

[891 

1892 5 

[893 

[894 

1895 

[896 B 

1897 

[898 

L899 

[900 B 



116.98 

99.11 

81.24 

63.37 

45.44 

27.57 

9.70 

351.82 

333.90 

316.03 

298.16 

280.29 

262.36 

244.49 

226.62 

208.75 

190.82 

172.95 

155.08 

137.21 

119.29 

101.42 

83.54 

65.67 

. 47.75 

29.88 

12.01 

354.13 

336.21 

318.34 

300.47 

282.60 

264.68 

246.80 

228.93 

211.06 

193.14 

175.26 

157.39 

139.52 

121.60 

103.73 

85.a5 

67.98 

50.06 

32.19 

14.31 

356.44 

338.52 



XL 



233.29 

336.72 

80.15 

183.58 
287.29 

30.72 

134.15 
237.58 
341.29 

84.72 

188.15 
291.67 

35.29 
138.72 
242.14 
345.57 

89.29 
192.71 
296.14 

39US7 
143.28 
246.71 
350.14 

93.57 
197.28 
300.71 

44.14 
147.57 
251.28 
354.71 

98.14 
201.57 
305.28 

48.71 
1.52.14 
255.57 
359.28 
102.71 
206.14 
309.56 

53.28 
156.71 
260.13 
3.56 
107.28 
210.70 
314.13 

57.56 
161.27 



XII. 



XIII. 



130.80 
50.76 
330.72 
250.68 
171.41 
91.37 
11.33 
291.29 
212.02 
131.98 
51.94 
331.90 
252.63 
172.59 
92.55 
12.51 
293.24 
213.20 
133.16 
53.12 
333.85 
253.81 
173.77 
93.74 
14.46 
294.42 
214.39 
134.35 
55.08 
335.04 
255.00 
174.96 
95.69 
15.65 
295.61 
215.57 
136.30 
56.26 
336.22 
256.18 
176.91 
96.87 
16.83 
206.79 
217.52 
137.48 
67.44 
337.40 
258.13 



2234(7 
52.55 
241.53 
70.52 
260.02 
89.01 
277.99 
106.98 
296.48 
125.46 
314.45 
143.43 
332.93 
161.92 
.150.91 
179.89 
9.39 
196.38 
27.37 
216.35 
45.85 
234.84 
63.83 
252.81 
82.32 
271.30 
100.29 
289.27 
118.78 
307.76 
136.75 
325.73 
155.23 
344.22 
173.20 
2.19 
191.69 
20.68 
209.66 
38.65 
228.15 
57.14 
246.12 
75.11 
264.61 
93.59 
282.56 
111.56 
301.07 



XIV. 



44.34 

167.16 
289.98 

52.79 
174.96 
297.78 

60.59 
183.41 
305.58 

^.40 
191.21 
314.03 

76.20 
J 99.01 
321.83 

84.65 
206.81 
329.63 

92.45 
215.27 
337.43 
100.25 
223.07 
345.89 
108.05 
230.67 
353.69 
116.50 
238.67 
1.49 
124.31 
247.12 
9.29 
132.11 
254.92 

17.74 
139.91 
262.73 

25.54 
148.36 
270*53 

33.34 
156.16 
278.96 

41.15 
163.96 
286.78 

49.60 
171.76 



XV. 



o 

4.1 
27.5 
50.9 
74.3 
98.7 
122.1 
145.5 
168.9 
193.3 
216.7 
240.1 
263.5 
287.9 
311.3 
334.7 
358.1 
22.5 
45.9 
G9.3 
92.7 
117.1 
140.5 
163.9 
187.3 
211.7 
235.1 
258.5 
281.9 
306.3 
329.7 
353.1 
16.5 
41.0 
64.4 
87.7 
111.1 
135^ 
159.0 
182.4 
205.7 
230.2 
253.6 
277j0 
300.4 
324.8 
348.2 
11.6 
35.0 
59.4 



XVI. 



219.5 
25.1 
190.7 
356.3 
161.3 
326.9 
132.5 
298.1 
103.2 
268.8 
74.4 
240.0 
45.0 
210.6 
16.2 
181.8 
346.9 
152.5 
318.1 
123.7 
288.7 
94.3 
259.9 
65.5 
230.6 
36.2 
201.6 
7.4 
172.4 
338.0 
143.6 
309.2 
114.3 
279.9 
65.5 
251.1 
56.1 
221.7 
27.3 
192.9 
356.0 
163.6 
329.2 
134.7 
299.8 
105.4 
271.0 
76.6 
241.7 



XVII. 



305.9 
268.7 
231.4 
194.1 
157.8 
120.5 
63.3 
46.0 
9.6 
332.4 
295.1 
257.6 
221.5 
184.2 
146.9 
109.7 
73.3 
36.0 
358.8 
321.5 
285.1 
247.9 
210.6 
173.4 
137.0 
99.7 
62.5 
25.2 
348.8 
311j6 
274.3 
237.0 
200.7 
163.4 
126.1 
88.9 
52.5 
15.2 
338.0 
300.7 
264.3 
227.1 
189.8 
152.6 
116.2 
78.9 
41.7 
4.4 
328.0 



xvni. 

28^3 
124.8 
221.3 
317.8 

55.5 
152.0 
248.5 
345.0 

82.7 
179.2 
275.7 

l2Ji 
110.0 
206.5 
303.0 

39.5 
137.2 
233.7 
330.2 

66.7 
164.4 
260.9 
357.4 

93.9 
191.6 
288.1 

24.6 
121.1 
218.9 
315.4 

51.9 
146.4 
246.1 
342.6 

79.1 
175.6 
273.3 

9.8 
106.3 
202.8 
300.5 

37.0 
133.5 
230.0 
327.8 
64.3 
160.8 
257.2 
355.0 



31 



• 






TABLE III.— Coniinued. 

FOB THE ARGUMENTS. 










A. 


For the difiereni Yean. 


The times are referred to the meridiaa of WaeUogtoa. 




Years. 


XIX. 


XX. 


XXI. 


XXII. 


xxin. 


XXIV. 


XXV 


XXVL 


xxvn. 







o 





o 


o 


o 


o 


o 


o 


18SQB 


316.3 


179.2 


346.2 


209.8 


267.9 


14.5 


322.0 


58.8 


83.0 


1853 


54.3 


245.4 


.48.4 


100.9 


219.7 


173.1 


311.0 


340.3 


77.6 


1854 


152.4 


311.6 


110.5 


352.1 


171.5 


331.8 


300.0 


261.8 


72.2 


1855 


250.4 


17.7 


172.7 


243.2 


123.3 


130.5 


289.2 


183.3 


66.8 


1^6 5 


348.6 


85.1 


234.0 


134.1 


75.0 


289.6 


277.2 


104.5 


61.3 


1857 


86.6 


151.2 


296.2 


25.2 


26.8 


88.2 


266.3 


26.0 


55.9 


1858 


184.7 


217.4 


358.4 


276.4 


.338.6 


246.9 


256.3 


307.5 


60.5 


1859 


282.7 


283.6 


60.5 


167.5 


290.4 


45.5 


244.4 


228.9 


45.1 


1860 B 


20.9 


350.9 


121.9 


58.4 


242.1 


204.6 


232.4 


150.2 


39.7 


1861 


118.9 


57.1 


184.1 


309.5 


193.9 


3.3 


221.5 


71.7 


34.2 


186d 


217.0 


123.2 


246.2 


200.7 


145.7 


162.0 


210.6 


353.2 


28.8 


1863 


315.0 


189.4 


808.4 


91.8 


97.5 


320.6 


199.6 


274.6 


23.4 


1864 B 


53.2 


256.7 


369.7 


342.7 


49.1 


^ 119.7 


187.7 


196.9 


18.0 


1865 


151.3 


322.9 


71.9 


233.8 


0.9 


278.4 


176.7 


117.4 


12.5 


1866 


249.3 


29.1 


134.1 


125.0 


312.7 


77.0 


165.8 


38.9 


7.1 


1867 


347.3 


95.2 


196.2 


16.1 


264.5 


235.7 


154.9 


320.3 


1.7 


1868 B 


85.5 


162.6 


257.6 


267.0 


216.2 


34.8 


142.9 


241.6 


356.3 


1869 


183.6 


228.7 


319.7 


158.1 


1^.0 


193.4 


132.0 


163.1 


350.8 


1870 


261.6 


294.9 


21.9 


49.3 


119.8 


352.1 


121.0 


84.5 


345.4 


1871 


19.6 


1.1 


84.1 


300.4 


71.6 


150.8 


llO.l 


6.0 


340.0 


1872 B 


117.9 


68.4 


145.4 


191.3 


23.3 


309.9 


96.2 


287.3 


334.6 


1873 


215.9 


134.6 


207.6 


82.4 


335.1 


108.5 


87.2 


208.8 


329.2 


1874 


313.9 


200.8 


269.8 


333.6 


286.9 


267.2 


76.3 


130.2 


323.7 


1875 


51.9 


266.9 


331.9 


224.7 


238.7 


65.8 


65.3 


51.7 


318J) 


1876 B 


150.2 


334.3 


33.3 


115.6 


190.4 


224.9 


53.4 


333.0 


312.9 


1877 


248,2 


40.4 


95.5 


6.8 


142.2 


23.6 


42.5 


254.5 


307.5 


1878 


346.2 


106.6 


157.6 


257.9 


94.0 


182.3 


31.5 


175.9 


302.0 


1879 


84.2 


172.8 


219.8 


149.0 


45.8 


340.9 


20.6 


97.4 


296.6 


1880 B 


182.5 


240.1 


281.1 


39.9 


357.5 


140.0 


8.6 


18.7 


291.2 


1881 


280.5 


806.3 


343.3 


291.1 


309.3 


298.7 


357.7 


300.2 


285.8 


1882 


18.5 


12.4 


45.5 


182.2 


261.1 


97.3 


346.8 


221.6 


260.4 


1883 


116.5 


78.6 


107.6 


73.4 


212.9 


256.0 


335.8 


143.1 


274.9 


1884 B 


214.8 


145.9 


169.0 


324.2 


164.5 


55.1 


. 323.9 


64.4 


269.5 


1885 


312.8 


212.1 


231.2 


215.4 


116.3 


213.7 


312.9 


345.9 


264.1 


1886 


60.8 


278.3 


293.3 


106.5 


68.1 


12.4 


302.0 


267.3 


258.7 


1887 


148.8 


344.4 


355.5 


357.7 


19.9 


171.1 


291.0 


188.8 


253.2 


1888 B 


247.1 


51.8 


56.8 


248.5 


331.6 


330.2 


279.1 


110.1 


247.8 


1889 


345.1 


118.0 


119.0 


139.7 


283.4 


128.8 


268.2 


31.5 


242.4 


1890 


83.1 


184.1 


181.2 


30.8 


235.2 


287.5 


257.2 


313.0 


237.0 


1891 


181.1 


250.3 


243.3 


282.0 


187.0 


86.1 


246.3 


234.5 


231.5 


1892 B 


279.4 


317.6 


304.7 


172.8 


138.7 


245.2 


234.3 


155.8 


226.1 


1893 


17.4 


23.8 


6.9 


64.0 


90.5 


43.9 


223.4 


77.2 


220.7 


1894 


115.4 


90.0 


69.0 


315.1 


42.3 


202.6 


212.5 


358.7 


215.3 


1895 


213.4 


156.1 


131.2 


206.3 


354.1 


1.2 


201.5 


280.2 


209.9 


1896 B 


311.7 


223.5 


192.5 


97.1 


305.8 


160.3 


189.6 


201.4 


204.4 


1897 


49.7 


289.6 


254.7 


348.3 


257.6 


319.0 


178.6 


122.9 


199.0 


1898 


147.7 


355.8 


316.9 


239.4 


209.4 


117.6 


167.7 


44.4 


193.6 


1899 


245.7 


62.0 


19.0 


130.6 


16K2 


276.3 


15&8 


325.9 


186.2 


1900 B 


344.0 


129.3 


80.4 


21.5 


112.8 


75.4 


144.8 


247.1 


162.7 



32 



TABLE Ul.—Cantimed. 

FOR THE ARGUMENTS. 

A* For the different Years. The times are referred to the meridian of Washington. 



Years. 



xxvni. 



1852 B 
1853 

1854 

1855 

1856 B 

1857 

1858 

1859 

1860 B 

1861 

1862 

1863 

1864 B 

1865 

1866 

1867 

1868 B 

1669 

1870 

1871 

1872 5 

1873 

1874 

1875 

1876 fi 

1877 

1878 

1879 

1880 B 

1881 

1882 

1883 

1884 B 

1885 

1886 

1887 

1888 B 

1889 

1890 

1891 

1892 B 

1893 

1894 

1895 . 

1896 B 
1897 
1898 
1899 
1900 B 



141.2 
196.4 
251.7 
306.9 
2.3 

57.5 
112.7 
168.0 
223.4 
278.6 
333.8 

29.0 

84.4 
139.6 
194.9 
250.1 
305.5 
0.7 

56.0 
111.2 
166.6 
221.8 
277.0 
332.3 

27.6 

82.9 
138.1 
193.3 
248.7 
304.0 
359.2 

54.4 
109.8 
165.0 
220.3 
275.5 
330.9 

26.1 

81.3 
136.6 
192.0 
247.2 
302.4 
357.6 

53.0 
108.3 
163.5 
218.7 
274.1 



XXIX. 



o 
171.1 

190.4 

209.7 

229.2 

247.7 

267.1 

286.4 

305.8 

324.3 

343.7 

3.1 

22.5 

40.9 

60.3 

79.7 

99.1 

117.5 

136.9 

156.3 

175.7 

194.1 

213.5 

232.9 

252.3 

270.8 

290.2 

309.5 

328.9 

347.4 

6.8 

26.2 

45.5 

64.0 

83.4 

102.8 

122.2 

140.6 

160.0 

179.4 

198.8 

217.3 

236.6 

256.0 

275.4 

293.9 

313.3 

332.6 

352.0 

10.5 



XXX. 



237.4 

4.2 

131.0 

257.8 

26.0 
152.8 
279.6 

46.4 
174.6 
301.4 

68.2 
195.0 
323.2 

90.0 
216.8 
343.7 
111.8 
238.6 
5.4 
132.3 
260.4 

27.2 
154.1 
280.9 

49.0 
175.8 
302.7 

69.5 
197.6 
324.5 

91.3 
218.1 
346.2 
113.1 
239.9 
366.7 
134.9 
261.7 

28.5 
155.3 
283.5 

50.3 
177.1 
303.9 

72.1 
198.9 
325.7 

92.5 
220.7 



XXXI. 



330.1 

6.0 

41.8 

77.7 

114.6 

150.4 

186,3 

222.1 

259.1 

294.9 

330.7 

6.6 

43.5 

79.4 

115.2 

151.0 

188.0 

^3.8 

259.7 

295.5 

332.4 

8.3 

44.1 

80.0 

116.9 

152.7 

188.6 

224.4 

261.3 

297.2 

333.0 

8.9 

45.8 

81.6 

117.5 

153.3 

190.2 

226.1 

261.9 

297.8 

334.7 

10.6 

46.4 

82.2 

119.2 

155.0 

190.8 

226.7 

263.6 



XXXII. 



107.3 
174.9 
242.6 
310.3 

18.2 

85.9 
153.5 
221.2 
269.1 
356.8 

64.5 
132.1 
200.0 
267.7 
335.4 

43.1 
110.9 
178.6 
246.3 
314.0 

21.9 

89.5 

157.2 

224.9 

292.8 

0.5 

68.2 
135.8 
203.7 
271.4 
339.1 

46.8 
114.6 
182.3 
250.0 
317.7 

25.6 

93.2 

160.9 

228.6 

296.5 

4.2 

71.8 
139.5 
207.4 
275.1 
342.8 

50.4 
118.3 



XXXIII. 



297.8 
213.7 
129.7 

45.6 
320.4 
236.3 
152.3 

68.3 
343.0 
259.0 
174.9 

90.9 

5.6 

281.6 

197.5 

113.5 

28.2 
304.2 
220.2 
136.1 

50.9 
326.8 
242.8 
158.7 

73.5 
349.4 
265.4 
181.4 

96.1 

]2.1 
288.0 
204.0 
118.7 

34.7 
310.7 
226.6 
141.4 

57.3 
333.3 
249.2 
164.0 

79.9 
355.9 
271.9 
186.6 
102.6 

18.5 
294.5 
209.2 



XXXIV. 



134.9 

78.2 

21.6 

324.9 

270.1 

213.5 

156.8 

100.2 

45.3 

348.7 

292.0 

235.4 

180.5 

123.9 

67.2 

10.6 

315.8 

IK9.1 

202.5 

145.8 

91.0 

34.3 

337.7 

281.0 

226.2 

169.6 

112.9 

56.3 

1.4 

304.8 

248.1 

191.5 

136.7 

80.0 

23.4 

326.7 

271.9 

215.2 

158.6 

101.9 

47.1 

350.4 

293.8 

237.1 

182.3 

125.6 

69.0 

12.4 

317.5 



XXXV. 

272^0 

247.2 

222.4 

197.6 

173.7 

148.9 

124.1 

99.3 

75.4 

50.6 

25.7 

0.9 

337.0 

312.2 

287.4 

262.6 

238.7 

213.9 

189.1 

164.3 

140.4 

115.6 

90.8 

66.0 

42.1 

17.3 

352.5 

327.7 

303.8 

279.0 

254.2 

229.4 

205.5 

180.7 

155.9 

131.1 

107.2 

82.4 

57.6 

32.8 

8.9 

344.1 

319.2 

294.4 

270.6 

245.7 

220.9 

196.1 

172.2 



XXXVI. 

110°.7 
340.9 
211.2 

81.4 
313.3 
183.5 

53.8 
284.0 
155.9 

26.1 
256.4 
126.6 
358.5 
228.7 

99.0 
329.2 
201.1 

71.3 
301.6 
171.8 

43.7 
274.0 
144.2 

14.4 
246.3 
116.6 
346.8 
217.1 

88.9 
319.2 
189.4 

59.7 
291.5 
161.8 

32.0 
262.3 
134.1 
4.6 
234.6 
104.9 
336.7 
207.0 

77.2 
307.5 
179.3 

49.6 
279.8 
150.1 

22.0 



33 







TABLE lll.—Coniimed. 








FOE THE ARGUMENTS. 






A. 


For &e diflTerent Yean. The times are referred to the meridian of Washington. 




Yean. 


XXX vu. 


xxxvin. 


YXVIX-. 


XTi. 


XLI. 


XLll. 


xun. 


XTJV. 


XTiV. 







o 


o 


o 


o 


o 


o 


o 


o 


1852 £ 


247.8 


189.6 


1 


286 


161 


103 


10 


214 


63 


1853 


149.9 


31.1 


221 


199 


266 


147 


146 


128 


8 


1854 


52.0 


232.5 


82 


112 


11 


192 


281 


43 


313 


1855 


314.0 


73.9 


903 


25 


116 


236 


56 


317 


258 


1856^ 


216.8 


275.9 


164 


300 


220 


279 


191 


233 


203 


1857 


118.9 


117.4 


24 


213 


325 


324 


326 


147 


148 


1858 


21.0 


318.8 


245 


126 


70 


8 


101 


62 


93 


1859 


283.1 


160.2 


106 


39 


175 


62 


237 


336 


38 


1860^ 


185.9 


2.2 


327 


313 


279 


96 


371 


252 


344 


1861 


88.0 


203.7 


187 


226 


24 


140 


147 


166 


288 


1862 


350.1 


45.1 


48 


140 


129 


184 


282 


81 


233 


1863 


252.2 


246.5 


269 


53 


234 


229 


57 


355 


178 


1864 B 


155.0 


88.5 


129 


327 


339 


272 


192 


271 


124 


1865 


57.1 


290.0 


350 


240 


84 


316 


327 


185 


69 


1866 


319.2 


131.4 


211 


153 


188 


1 


102 


100 


14 


1867 


221.3 


332.8 


72 


67 


293 


45 


238 


14 


318 


1868 B 


124.1 


174.8 


292 


341 


38 


88 


12 


290 


264 


1869 


26.2 


16.3 


153 


254 


143 


133 


148 


204 


209 


1870 


288.2 


217.7 


14 


167 


248 


177 


283 


119 


154 


1871 


190.3 


59.2 


235 


80 


352 


221 


58 


33 


99 


1872 B 


93.1 


261.1 


95 


355 


97 


265 


193 


306 


44 


1873 


355.2 


102.6 


316 


268 


202 


309 


328 


223 


349 


1874 


257.3 


304.0 


177 


181 


307 


353 


103 


138 


294 


1875 


159.4 


145.5 


38 


94 


52 


38 


339 


52 


239 


1876 B 


62.2 


347.4 


258 


9 


156 


81 


13 


327 


185 


1877 


324.3 


188.9 


119 


282 


261 


125 


148 


262 


130 


1878 


226.4 


30.3 


340 


195 


6 


170 


264 


156 


74 


1879 


128.5 


231.8 


201 


108 


111 


214 


59 


71 


19 


1880 B 


31.3 


73.8 


61 


23 


215 


257 


194 


346 


325 


1881 


293.4 


275.2 


282 


296 


320 


302 


329 


261 


270 


1882 


195.5 


116.6 


143 


209 


65 


346 


104 


175 


215 


1883 


97.6 


318.1 


4 


122 


170 


30 


239 


90 


160 


1884 B 


0.4 


160.1 


224 


37 


274 


74 


14 


5 


105 


1885 


262.5 


1.5 


85 


310 


19 


118 


149 


280 


50 


1886 


164.5 


202.9 


306 


223 


124 


162 


285 


194 


355 


1887 


66*6 


44.4 


166 


136 


229 


207 


60 


109 


300 


1888 B 


329.4 


306.4 


27 


50 


333 


250 


195 


23 


246 


1889 


231.5 


87.8 


248 


323 


78 


294 


330 


299 


191 


1890 


133.6 


289.2 


109 


236 


183 


339 


105 


213 


135 


1891 


'35.7 


130.7 


329 


149 


288 


23 


240 


128 


80 


1892 B 


298.5 


332.7 


190 


64 


32 


66 


15 


43 


26 


1893 


200.6 


174.1 


51 


337 


137 


111 


150 


318 


331 


1894 


102.7 


15.5 


272 


250 


242 


155 


286 


232 


276 


1895 


4.8 


217.0 


132 


163 


347 


199 


61 


147 


221 


1896 fi 


267.6 


59.0 


353 


78 


91 


243 


195 


62 


166 


1897 


169.7 


260.4 


214 


351 


196 


287 


331 


336 


111 


1898 


71.8 


101.8 


74 


, 264 


301 


331 


106 


251 


56 


1899 


333.8 


303.3 


295 


177 


46 


15 


241 


166 


1 


1900 B 


236.7 


145.3 


156 


92 


150 


59 


16 


81 


307 



34 









TABLE III.— Contimed. 














FOR 


THE ARGUMENTS. 








B« Yariatioos of the Ailments for the different Months 


. The timet 




Months. 


L 


IL 


TTT. 


IV. 


V. 


VI. 


Vll. 


vni. 


IX. 


January 


o!ooo 


o!ooo 


o!ooo 


o!oo 


0°00 


d'.oo 


0°.00 


0°.00 


o!oo 


February 


357.4^ 


6.209 


1.058 


3.63 


9.85 


21.20 


14.99 


346.07 


348.64 


March 


355.098 


11.817 


2.014 


6.91 


18.74 


40.35 


28.53 


333.48 


338.38 


April 


352.523 


18.026 


3.072 


10.54 


28.59 


61.55 


43.52 


319.55 


327.02 


May 


350.031 


24.035 


4.096 


14.06 


38.12 


82.07 


58.03 


306.07 


316.03 


June 


347.456 


30.244 


5.154 


17.69 


47.97 


103.27 


73.02 


292.14 


304.67 


July 


344.964 


36.253 


6.178 


21.21 


57.50 


123.79 


87.53 


278.66 


293.68 


August 


342.389 


42.462 


7.236 


24.84 


67.35 


144.99 


102.52 


264.73 


282.32 


September 


339.814 


48.671 


8.294 


28.47 


77.19 


166.19 


117.51 


250.80 


270.96 


October 


337.322 


54.680 


9.318 


31.99 


86.72 


186.71 


132.02 


237.32 


259.97 


November 


334.747 


60.889 


10.376 


35.62 


96.57 


207.91 


147.01 


223.39 


248.61 


December 


332.255 


66.898 


11.400 


39.14 


106.10 


228.43 


161.52 


209.91 


237.62 


Months. 


X. 


XI. 


XII. 


XIII. 


XIV. 


XV. 


XVI. 


XVIT. 


xvin. 


January 


0°.00 


o'loo 


o°.oo 


0°.00 


0°.00 




0.0 




0.0 


o 
0.0 


o 
0.0 


February 


358.48 


8.78 


23.78 


16.05 


339.85 


32.6 


343.5 


27.4 


38.8 


March 


357.11 


16.72 


. 45.26 


30.55 


321.65 


62.0 


328.6 


52.2 


73.8 


April 


355.59 


25.50 


69.04 


46.60 


301.50 


94.6 


312.1 


79.6 


112.6 


May 


354.12 


34.00 


92.05 


62.13 


282.00 


126.1 


296.1 


106.1 


150.1 


June 


352.60 


42.78 


115.83 


78.18 


261.85 


158.7 


279.6 


133.5 


188.9 


July 


351.13 


51.28 


138.84 


93.71 


242.35 


190.2 


263.6 


160.0 


226.4 


August 


349.61 


60.06 


162.62 


109.76 


222.20 


222.8 


247.1 


187.4 


265.2 


September 


348.09 


68.84 


186.39 • 


125.81 


202.05 


255.3 


230.6 


214.8 


303.9 


October 


346.62 


77.34 


209.40 


141.34 


182.55 


266.8 


214.6 


241.3 


341.4 


November 


345.10 


86.12 


233.18 


157.39 


162.40 


319.4 


198.1 


263.7 


20.2 


December 


343.63 


94.62 


256.19 


172.92 


142.90 


350.9 


182.1 


295.3 


57.7 


Months. 


XIX. 


XX. 


XXT. 


XXII. 


XXIU. 


XXIV. 


XXV. 


XXVI. 


xxvu. 


January 


o 
0.0 


o 
0.0 


o 

0.0 


o 
0.0 


o 
0.0 


o 

0.0 


o 
0.0 


o 
0.0 


o 

0.0 


February 


8.3 


36.2 


334.7 


350.8 


355.9 


13.5 


328.5 


353.3 


359.5 


March 


15.8 


68.9 


311.9 


342.4 


352.2 


25.6 


300.1 


347.3 


359.1 


April 


24.1 


105.1 


286.6 


333.2 


348.1 


39.1 


268.6 


340.6 


358.6 


May 


32.2 


140.1 


262.1 


324.2 


344.1 


52.2 


238.1 


334.2 


358.2 


June 


40.5 


176.3 


236.8 


315.0 


340.0 


65.6 


206.6 


327.5 


357.7 


July 


48.6 


211.3 


212.3 


306.1 


336.0 


78.7 


176.1 


321.0 


357.3 


August 


56.9 


247.5 


187.0 


296.8 


331.9 


92.1 


144.6 


314.3 


356.8 


September 


65.2 


283.7 


161.7 


287.6 


327.8 


105.6 


113.1 


307.6 


356.3 


October 


73.3 


318.7 


137.2 


278.6 


323.8 


118.6 


82.6 


301.2 


355.9 


November 


81.6 


354.9 


111.9 


269.4 


319.7 


132.1 


51.1 


294.5 


355.4 


December 


89.7 


29.9 


87.4 


260.5 


315.7 


145.2 


20.6 


288.0 


355.0 




In 


Bissextile 1 


fears subtnu 


:t one day fi 


rom the date 


> in the first 


two months 


■ 





35 





TABLE III. Continued. 


- 






FOR 


THE ARGUMENTS. 


* 




B. Variations of the Arguments for the difierent Months 


. The times are referred to the meridian of Washington. 1 


Months. 


XXVIIL 


XXIX. 


XXX. 




XXXTT. 


xxxni. 


XXXIV. 


XXXV. 


XXXVI. 


XXXI. 


Jannary 


o 
0.0 


o 
0.0 


o 
0.0 


o 
0.0 


o 
0.0 


o 
0.0 


o 

0.0 


o 
0.0 


o 
0.0 


February 


4.7 


331.1 


41.3 


33.6 


5.7 


322.3 


56.3 


28.5 


50.1 


March 


6.9 


304.9 


78.7 


64.0 


10.9 


288.3 


107.2 


54.2 


95.4 


April 


13.5 


276.0 


120.0 


97.6 


16.6 


250.6 


163.5 


82.6 


145.5 


May 


18.0 


248.0 


160.0 


130.2 


22.2 


214.1 


218.0 


110.2 


194.0 


Jane 


22.7 


219.1 


201.3 


163.8 


27.9 


176.4 


274.4 


138.6 


244.1 


July 


27.2 


191.1 


241.3 


196.4 


33.5 


139.9 


328.9 


166.2 


292.6 


August 


31.8 


162.2 


282.6 


230.0 


39.2 


102.2 


25.2 


194.6 


342.7 


September 


36.5 


133.3 


323.9 


263.6 


44.9 


64.5 


81.6 


223.1 


32.8 


October 


41.0 


105.3 


3.9 


296.2 


50.5 


28.0 


136.1 


250.6 


81.3 


November 


45.6 


76.4 


45.2 


329.8 


56.2 


350.3 


192.4 


279.1 


131.4 


December 


50.1 


48.4 


85.2 


2.4 


61.8 


313.8 


246.9 


306.6 


179.9 


Months. 


XXXVIL 


xxxvin. 


XXXIX. 


XL. 

1 


XIJ. 


XLII. 


XLTTT. 


XLIV. 


XLV. 


January 
February 


o . 

0.0 
22.3 


o 

0.0 
17.1 


o 


348 


o 


54 


o 


338 


o 


333 


o 


341 


o 


23 


o 


26 


March 


42.4 


32.5 


338 


102 


319 


309 


324 


44 


50 


April 


64.6 


49.6 


326 


156 


297 


282 


305 


67 


76 


May 


86.2 


66.2 


314 


208 


276 


256 


286 


90 


101 


June 


108.4 


83.3 


303 


262 


254 


229 


267 


113 


127 


July 


130.0 


99.9 


291 


314 


233 


203 


248 


136 


152 


August 


152.2 


117.0 


279 


7 


212 


177 


229 


159 


.178 


September 


174.5 


134.1 


268 


61 


190 


150 


210 


182 


204 


October 


196.0 


150.6 


256 


113 


169 


124 


192 


205 


229 


November 


218.3 


167.7 


244 


167 


147 


97 


173 


228 


255 


December 


239.8 


184.3 


233 


219 


126 


71 


154 


250 


280 


/ 


In Bissextile Tears snbtnu 


;t one day fi 


pom the date in the first two months 


* 






• 











36 





■ 




TABLE III.— OnHnued. 


» 












FOR 


THE ARGUMENTS. 








C« Variattons of the Aiigameiits for the difierent Dajs. 


The times 


are refened to the meridiaii of Washington. 1 


Days. 


L 


n. 


m. 


IV. 


V. 


VI. 


vu. 


viir. 


IX. 


1 


359!917 


0^200 


o!o34 


o 
0.12 


0.32 


o'!68 


o''.48 


359'!55 


359.63 


2 


359.834 


0.401 


0.068 


0.23 


. 0.64 


1.37 


0.97 


359.10 


359.27 


3 


359.751 


0.601 


0.102 


0.35 


0.95 


2.05 


1.45 


358.65 


358.90 


4 


359.667 


0.801 


0.137 


0.47 


1.27 


2.74 


1.93 


358.20 


358.53 


5 


359.584 


1.001 


0.171 


0.59 


1.59 


3.42 


2.42 


357.75 


358.17 


6 


359.501 


1.202 


0.205 


0.70 


1.90 


4.10 


2.90 


357.30 


357.80 


7 


359.418 


1.402 


0.239 


0.82 


2.22 


4.79 


3.39 


356.85 


357.43 


8 


359.335 


1.602 


0.273 


0.94 


2.54 


5.47 


3.87 


356.40 


357.07 


9 


359.252 


1.803 


0.307 


1.06 


2.86 


6.16 


4.35 


355.95 


356.70 


10 


359.169 


2.003 


0.341 


1.17 


3.18 


6.84 


4.84 


355.51 


356.34 


UO 


358.338 


4.006 


0.683 


2.34 


6-35 


13.68 


9.67 


351.01 


352.67 


30 


357.508 


6.009 


1.024 


3.52 


9.53 


20.52 


14.51 


346.52 • 


849.01 


Days. 


X. 


XI. 


XTT. 


Xlll. • 


XIV. 


XV. 


XVI. 


XVU. 


XVlll. 


1 


359^95 


o''.28 


o 
0.77 


o!52 


359^35 


o 

1.1 


S59'!5 




0.9 


o 

1.3 


2 


359.90 


0.57 


1.53 


1.04 


358.70 


2.1 


358.9 


1.8 


2.5 


3 


359.85 


0.85 


2.30 


1.55 


358.05 


3.2 


358.4 


2.7 


3.8 


4 


359.80 


1.13 


3.07 


2.07 


357.40 


4.2 


357.9 


3.5 


5.0 


5 


359.76 


1.42 


3.84 


2.59 


356.75 


5.3 


357.3 


4.4 


6.8 


6 


350.71 


1.70 


4.60 


3.11 


856.10 


6.3 


356.8 


5.3 


7.6 


7 


359.66 


1.98 


5.37 


3.62 


855.45 


7.4 


356.3 


6.2 


8.8 


8 


359.61 


2*27 


6.14 


4.14 


354.80 


8.4 


855.7 


7.1 


10.0 


9 


350.56 


2.55 


6.90 


4.66 


354.15 


9.5 


355.2 


8.0 


11.3 


10 


359.51 


2.83 


7.67 


5.18 


353.50 


10.5 


354.7 


8.8 


12.5 


20 


359.02 


6.67 


15.34 


10.36 


347.00 


21.0 


349.4 


17.7 


85.0 


30 


358.53 


8.50 


23.01 


15.53 


340.50 


31.5 


344.0 


26.5 


37.5 


Days. 


XIX. 


XX. 


XXL 


XXTT. 


XXlll. 


XXIV. 


XXV. 


X X VI. 


XXVll. 


1 


o 
0.3 


o 

1.2 


359^2 


359^7 


359°9 




0.4 


359!o 


359°8 


o 
0.0 


2 


0.5 


2.3 


358.4 


359.4 


359.7 


0.9 


358.0 


359.6 


0.0 


3 


0.8 


3.5 


357.6 


359.1 


359.6 


1.3 


356.9 


359.4 


0.0 


4 


1.1 


4.7 


356.7 


358.8 


359.5 


1.7 


355.9 


359.1 


359.9 


5 


1.3 


5.8 


355.9 


358.5 


359.3 


2.2 


354.9 


358.9 


359.9 


6 


1.6 


7.0 


355.1 


358.2 


359.2 


2.6 


353.9 


358.7 


359.9 


7 


1.9 


8.2 


354.3 


357.9 


359.1 


3.0 


352.9 


358.5 


359.9 


8 


2.2 


9.3 


353.5 


357.6 


358.9 


3.5 


351.9 


358.3 


359.9 


9 


2.4 


10.5 


352.7 


357.3 


358.8 


3.9 


350.9 


358.1 


359.9 


10 


2.7 


11.7 


351.8 


357.0 


358.7 


4.4 


349.8 


357.9 


359.9 


20 


5.4 


23.4 


343.7 


354.0 


357.4 


8.7 


339.7 


355.7 


359.7 


30 


8.1 


35.0 


335.5 


351.1 


356.0 


13.0 


320.5 


353.6 


359.6 



37 









TABLE III.— amtimed. 


• 








FOR THE ARGUMENTS. 




C« Variations of ihe Aiigiiments for the different Dajs. The times are referred to die meridian of Washington. 1 


Dajs. 


XXVIll. 


XXTX. 


XXX 


XX XT. 


XXXII. 


xxxni. 


XXXIV. 


XXXV. 


XXXVI. 




o 


o 


o 


o 


o 


o 


o 


o 


o 


1 


0.2 


359.1 


1.3 


1.1 


0.2 


358.8 


1.8 


0.9 


1.6 


2 


0.3 


358.1 


2.7 


2.2 


0.4 


a57.6 


3.6 


1.8 


3.2 


3 


0.5 


357.2 


4.0 


3.3 


0.6 


356.3 


5.5 


2.8 


4.9 


4 


0.6 


356.3 


5.3 


4.3 


0.7 


355.1 


7.3 


3.7 


6.5 


5 


0.8 


355.3 


6.7 


5.4 


0.9 


353.9 


9.1 


4.6 


8.1 


6 


0.9 


354.4 


8.0 


6.5 


1.1 


te2.7 


10.9 


5.5 


9.7 


7 


1.1 


353.5 


9.3 


7.6 


1.3 


351.5 


12.7 


6.4 


11.3 


8 


1.2 


352.5 


10.7 


8.7 


1.5 


350.3 


14.5 


X 7.3 


12.9 


9 


1.4 


351.6 


12.0 


9.8 


1.7 


349.0 


16.4 


8.3 


14.6 


• 10 


1.5 


350.7 


13.3 


10.9 


1.9 


347.8 


18.2 


9.2 


16.2 


20 


3.0 


341.3 


26.7 


21.7 


3.7 


335.7 


36.3 


18.4 


32.3 


30 


4.5 

• 


332.0 


40.0 


32.6 


5.6 


323.5 


54.5 


27.5 


48.5 


"Days. 


xxxvn. 


XXX vm. 


X X XIX. 


XL. 


XIJ. 


XLII. 


XTJn. 


X LIV. 


XLV. 




o 


o 


o 


o 


o 


o 


o 


o 


o 


1 


0.7 


0.6 





2 


359 


359 


359 


1 


1 


2 


1.4 


1.1 


359 


3 


359 


358 


359 


2 


2 


3 


2.2 


1.7 


359 


5 


358 


357 


358 


2 


3 


4 


2.9 


2.2 


359 


7 


357 


357 


358 


3 


3 


5 


3.6 


2.8 


358 


9 


357 


356 


357 


4 


4 


6 


4.3 


3.3 


358 


10 


356 


355 


356 


5 


5 


7 


5.0 


3.9 


357 


12 


355 


354 


356 


5 


6 


8 


5.7 


4.4 


357 


14 


354 


353 


355 


6 


7 


9 


6.5 


5.0 


357 


16 


354 


352 


354 


7 


8 


10 


7.2 


5.5 


356 


17 


353 


351 


354 


8 


8 


20 


14.4 


11.0 


352 


35 


346 


343 


348 


15 


17 


30 

1 


21.5 


16.6 

• 


349 


52 

• 


339 


334 


342 


23 


25 

■ 



38 









TABLE lll.—Coniinued. 






• 








FOR THE ARGUMENTS. 








D. Variations of the Ailments for thd difierent Honn. The times are reibrred to the meridian of Washlngtoti. 1 


Hours. 


L 


n. 


ni. 


IV. 


V. 


VI. 


vn. 


vm. 


TX. 


1 


359!997 


o!o08 


o!ooi 


o!oo 


0°.01 


o!o3 


0°.02 


359°.98 


359^99 


2 


359.993 


0.017 


0.003 


0.01 


0.03 


0.06 


0.04 


359.96 


359.97 


3 


359.990 


0.025 


0.004 


0.02 


0.04 


0.09 


0.06 


359.94 


359.95 


4 


359.986 


0.033 


0.006 


0.02 


0.05 


0.11 


0.08 


359.92 


359.94 


5 


359.983 


0.042 


0.007 


0.03 


0.07 


0.14 


0.10 


359.90 


359.92 


6 


359.979 


0.050 


0.008 


0.03 


0.08 


0.17 


0.12 


359.89 


359.91 


7 


359.976 


0.058 


0.010 


0.03 


0.09 


0.20 


0.14 


359.87 


359.89 


8 


359.972 


0.066 


0.011 


0.04 


0.11 


0.23 


0.16 


359.85 


359.88 


9 


359.969 


0.075 


0.013 


0.04 


0.12 


0.26 


0.18 


359.83 


359.86 


10 


359.965 


0.083 


0.014 


0.05 


0.13 


0.29 


0.20 


359.81 


35$r.85 


20 


359.930 


0.166 


0.028 

« 


0.10 


0.26 


0.57 


0.40 


359.62 


859.70 


Hoars. 


X. 


XI. 


XII. 


Xlll. 


XIV. 


XV. 


XVI. 


XVll. 


XV 111. 


1 


o°.oo 


0°.01 


0°.03 


o'!02 


359°.97 


o 
0.0 


o 
0.0 




0.0 


o 
0.1 


2 


0.00 


0.02 


0.06 


0.04 


359.95 


0.1 


0.0 


0.1 


0.1 


3 


359.99 


0.04 


0.10 


0.07 


359.92 


0.1 


359.9 


0.1 


0.2 


4 


359.99 


0.05 


0.13 


0.09 


359.89 


• 0.2 


359.9 


0.2 


0.2 


5 


359.99 


0.06 


0.16 


0.11 


359.87 


0.2 


359.9 


0.2 


0.3 


6 


359.99 


0.07 


0.19 


0.13 


359.84 


0.3 


359.9 


0.2 


0.3 


7 


359.99 


0.08 


0.22 


0.15 


359.81 


0.3 


359.9 


0.3 


0.4 


8 


359.98 


0.10 


0.26 


0.17 


359.78 


0.4 


359.8 


0.3 


0.4 


9 


359.98 


0.11 


0.29 


0.20 


359.76 


0.4 


359.8 


0.3 


0.5 


10 


359.98 


0.12 


0.32 


0.22 


359.73 


0.4 


359.8 


0.4 


0.5 


20 


359.96 


0.24 


0.64 


0.24 


359.46 


0.9 


359.6 


0.7 


1.0 


Hoars. 


XIX. 


XX. 


XXI. 


X\ll. 


XXIII. 


XXIV. 


XXV. 


XXVI. 


xxvn. 


1 

• 


o 

0.0 


o 
0.0 


o 

0.0 


o 

0.0 


o 
0.0 


o 
0.0 


o 

0.0 


o 

0.0 


o 
0.0 


2 


0.0 


0.1 


359.9 


0.0 


0.0 


0.0 


359.9 


0.0 


0.0 


3 


0.0 


0.2 


359.9 


0.0 


0.0 


0.1 


359.9 


0.0 


0.0 


4 


0.0 


0.2 


359.9 


0.0 


0.0 


0.1 


359.8 


0.0 


0.0 


5 


0.1 


0.2 


359.8 


359.9 


0.0 


0.1 


359.8 


0.0 


0.0 


6 


0.1 


0.3 


359.8 


359.9 


0.0 


0.1 


359.8 


0.0 


0.0 


7 


0.1 


0.3 


359.8 


359.9 


0.0 


0.1 


359.7 


0.0 


0.0 


8 


0.1 


OA 


359.7 


359.9 


0.0 


0.1 


359.7 


0.0 


0.0 


9 


0.1 


0.4 


359.7 


359.9 


0.0 


0.2 


359.6 


0.0 


0.0 


10 


0.1 


0.5 


359.7 


359.9 


0.0 


0.2 


359.6 


0.0 


0.0 


20 


0.2 


1.0 


359.3 


359.8 


0.0 


0.4 


359.2 


0.0 


0.0 



39 









TABLE III. Concluded. 




• 










FOR THE ARGUMENTS. 








D. Variations of the Ailments for the difFeront Hours. The times are referred to the meridian of Washington. 1 


Hoars. 


XX vm. 


XXTX. 


XXX. 


xxxr. 


XXXII. 


JLXXlll. 


XXXI V. 


XXXV. 


XX XVI. 




o 


o 


o 


o 


o 


o 


o 


o 


o 


1 


OJO 


0.0 


0.1 


0.0 


0.0 


359.9 


0.1 


0.0 


0.1 


2 


OjO 


359.9 


0.1 


0.1 


0.0 


359.9 


0.2 


0.1 


0.1 


3 


0.0 


359.9 


0.2 


0.1 


0.0 


359.8 


0.2 


0.1 


0.2 


4 


0.0 


359.8 


0.2 


0.2 


0.0 


359.8 


0.3 


0.2 


0.3 


5 


0.0 


359.8 


0.3 


0.2 


0.0 


359.7 


0.4 


0.2 


0.3 


6 


0.0 


359.8 


0.3 


0.3 


0.1 


359.7 


0.5 


0.2 


0.4 


7 


0.0 


359.7 


04 


0.3 


0.1 


359.6 


0.5 


0.3 


0.5 


8 


0.0 


359.7 


0.5 


0.4 


0.1 


359.6 


0.6 


0.3 


0.5 


9 


0.0 


359.7 


0.5 


0.4 


0.1 


359.5 


0.7 


0.3 


0.6 


10 


0.0 


359.6 


0.6 


0.5 


0.1 


359.5 


0.8 


0.4 


0.7 


20 


0.0 


359.2 


1.1 

— r 


0.9 


0.2 


359.0 


1.5 


0.8 


1.3 


Hoars. 


XXX vu. 


XXXVIII. 


XXXTX. 


XL. 


XIJ. 


XLll. 


XLIll. 


XMV. 


XLV. 




o 


o 


o 





o 


o 


o 


o 


o 


1 


0.0 


0.0 























2 


0.1 


0.1 























3 


0.1 


0.1 























4 


0.1 


0.1 























5 


0.2 


0.1 























6 


0.2 


0.1 























7 


0.2 


0.2 























8 


0.2 


0.2 





1 

















9 


0.3 


0.2 





1 


0' 














10 


0.3 


0.2 





1 

















20 


0.6 


0.5 





1 


359 


359 




• 


1 


1 



40 



TABLE IV. 

PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. 

Tenns multiplied with t Ailment = M. 



Arg. 




1 
2 
3 

4 
5 

6 

7 
8 
9 

10 
11 
12 
13 
14 
15 
16 
17 
18 
19 

20 

22 
23 
24 
25 
26 
27 
28 
29 

30 
31 
32 
33 
34 
35 
36 
37 
38 
39 

40 
41 
42 
43 
44 
45 



- 5.24 

+ 9.15 

23.51 

37.83 

52.09 

66.27 

80.37 

94.35 

108.20 

121.91 

+135.47 
148.84 
162.03 
175.01 
187.77 
200.31 
212.60 
224.65 
236.45 
247.98 

+259.22 

270.19 
280.86 
291.23 
301.29 
311.04 
320.46 
329.56 
338.32 
346.74 

354.83 
+362.62 
370.07 
377.21 
384.01 
360.48 
396.63 
402.45 
407.95 
413.13 

+418.00 
422.57 
426.82 
430.78 
434.45 

+437.82 



Diff. 



Vi 



+14.89 
14*86 
14*39 
14*36 
14*18 
14*10 
18*98 
18*86 
18*71 

18*66 

+18*87 
18*19 
ia.98 
12*76 
13*54 
13*39 
13*05 
11*80 
11*58 

11*34 

+10*97 

10*97 

10*87 

10*06 

9*76 

9*43 

9*10 

8*76 

8.43 

8*09 

+ 7.79 
7.45 
7*14 
6*80 
6*47 
6*15 
5*83 
6*50 
6.18 

4*87 

+ 4*57 
4*35 
8*96 
8*67 

+ 8*37 



-684.22 
683.87 
683.09 
681.86 
680.23 
678.17 
675.69 
672.80 
669.51 
665.82 

-661.73 
657.27 
652.42 
647.19 
641.62 
635.69 
629.42 
622.84 
615.94 
608.74 

-601.26 
593.51 
585.50 
577.25 
568.77 
560.07 
551*17 
542*08 
532.81 
523*39 

-513.81 
504.09 
494.25 
484.30 
474.25 
464.12 
453.91 
443.65 
433.35 
423.01 

-412.65 
402.27 
391.88 
381.49 
371.11 

-360.75 



Diff. 


& 


Diff. 


Arg. 




-35.71 





45 


+ 0*85 


34.59 


+1*13 


46 


0*78 


33.45 


1*14 


47 


1*31 


32.29 


1*16 


43 


1*65 


31.11 


1*18 


49 


3*06 


29.91 


1*30 


50 


3*48 


28.69 


1*33 


51 


3*89 


27.45 


1.34 


52 


8*39 


26*19 


1*36 


53 


8*69 


24*92 


1*27 


54 


4*09 




1*39 






-23.63 




55 


+ 4*46 


22.33 


+1*80 


56 


4*86 


21.01 


1*33 


67 


5*38 


19.68 


1*33 


58 


5*67 


18.34 


1*34 


59 


5*93 


16*99 


1*85 


60 


6*37 


15*63 


1*86 


61 


6*58 


14.25 


1*88 


62 


6*90 


12.67 


1-38 


63 


7*30 


11.48 


1*89 


64 


7*48 




1*89 






-10.09 




65 


+ 7.75 


8.69 


+1*40 


66 


8*01 


7.28 


1-41 


67 


8*36 


5.87 


1*41 


68 


8*48 


4.45 


1*43 


69 


8*70 


3.03 


1*43 


70 


8*90 


1*61 


1*43 


71 


9*09 


- 0.19 


1*43 


72 


9*37 


+ 1.23 


1*43 


73 


9*43 


2.65 


1*43 


74 


9*58 




1*43 






+ 4.07 




75 


+ 9*73 


5.48 


+1*41 


76 


9*84 


6.90 


1*43 


77 


9*95 


8.31 


1*41 


78 


10*05 


9.71 


1*40 


79 


10*18 


11.11 


1*40 


80 


10*31 


12.51 


1*40 


81 


10*36 


13.89 


1*38 


82 


10*30 


15.27 


1*38 


83 


10*34 


16.65 


1*88 


84 


10*36 




1*36 






+18.01 




85 


+10*38 


19.37 


+1*36 


86 


10*89 


20.72 


1*85 


87 


10*89 


22.05 


1*83 


88 


10*88 


23.38 


1-33 


89 


+10*86 


+24.69 


+1*31 


90 



li 


Diff. 


+437.82 




440.91 


+8*09 


443.73 


3*83 


446.27 


3*54 


448.56 


3*89 


450.58 


3*03 


452.36 


1*78 


453.68 


1*63 


455.17 


1*39 


456.22 


1*05 




0*83 


+457.04 




457.64 


+0*60 


458.02 


0*88 


458.19 


Vo.17 


456.16 


-0-08 


457.94 


0*33 


457.53 


0*41 


456.94 


0*59 


456.17 


0*77 


455.23 


0*94 




1*11 


+454.12 




452.a') 


-1*27 


451.42 


1*43 


449.84 


1*58 


446.12 


1*73 


446.26 


1*66 


444.26 


3*00 


442.13 


3*13 


439.88 


3*35 


437.51 


3*87 




3*49 


+435.02 




432.42 


-3*60 


429.72 


3*70 


426*92 


3*80 


424.02 


3*90 


421.02 


3*00 


417.93 


8*09 


414.76 


3*17 


411.50 


8*36 


408.17 


3*83 




8*41 


+404.76 




401.29 


-3*47 


397.75 


3*54 


394.14 


8*61 


390.47 


3*67 


+386*75 


-3*73 



Vi 



-360*75 
350.43 
340.15 
329.91 
319.74 
309.63 
299.58 
289.61 
279.72 
269.90 

-260.17 
250.53 
240.98 
231.53 
222.18 
212.93 
203.79 
194.75 
165.62 
177.01 

-168.31 
159.72 
151.25 
142.89 
134.65 
126*53 
118.54 
110.66 
102*91 
95.28 

- 87.77 
80.39 
73.12 
65.98 
58.96 
52.07 
45.29 
38.64 
32.10 
25.68 

- 19.38 
13.20 

7.13 

- 1.18 
+ 4.66 
+ 10.39 



Diff. 


il 




+24*69 


+10*32 


26.00 


10*28 


27.29 


10*24 


28.57 


10*17 


29.64 


10*11 


31.10 


10*05 


32.34 


9-97 


33.57 


9*69 


34.79 


9*82 


35.99 


9*78 






+37.17 


+ 9-64 






38.34 


9*55 






39.50 


9*45 


40.64 


9*35 






41.77 


9*25 


42.86 


9*14 






43.97 


9*04 






45.05 


8*98 


46.11 


8*81 






47.15 


8*70 






+48.18 


+ 8*59 






49.19 


8*47 


50.16 


8*36 


51.16 


8*24 






52.12 


8*12 






53.06 


7*99 


53.96 


7*88 


54.69 


7*75 


55.78 


7*63 


56*65 


7*51 






+57.50 


+ 7*38 


56.33 


7*27 


59.15 


7*14 


59.94 


7*02 


60.72 


6*89 


61*46 


6*78 


62.23 


6*C5 


62.95 


6*54 


63.66 


6*42 


64.35 


6*80 






+6^.02 


+ 6*18 


65.67 


6*07 


66*30 


5*95 


66.92 


5*84 


67.51 


+ 5*78 


4^.09 



Diff. 



+1*81 
1*29 
1*38 
1*27 
1*26 
1*34 
1*23 
1*22 
1*30 

1*18 

+1*17 
1*16 
1*14 
1*18 
1*11 
1*09 
1*06 
1*06 
1*04 

1*08 

+1-01 
0*99 
0*98 
0*96 
0*94 
0*92 
0*91 
0*89 
0*87 

0*85 

+0*88 
0*83 
0*79 
0*79 
0*76 
0*75 
0*72 
0*71 
0-69 

0*67 

+0.65 
0-68 
0.62 
0*59 

+0.68 



41 



TABLE lY .—CmOinued. 

PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. 

Terms multiplied with t. Aigameat = M. 



Aiig. 



90 
91 
92 
93 
94 
95 
96 
97 
98 
99 

100 
101 
102 
103 
104 
105 
106 
107 
108 
109 

110 
111 
112 
113 
114 
115 
116 
117 
118 
119 

120 
121 
.122 
123 
124 
125 
126 
127 
128 
129 

130 
131 
132 
133 
134 
135 



+386.75 
382.97 
379.14 
375.26 
371.33 
367.37 
363.36 
359.31 
355.23 
351.11 

+346.96 
342.78 
338.58 
334.35 
330.09 
325.81 
321.51 
317.19 
312.85 
308.50 

+304.13 
299.75 
295.35 
290.94 
286.52 
282.09 
277.66 
273.21 
269.76 
264.30 

+259.84 
255.37 
250.89 
246.42 
241.94 
237.46 
232.97 
228.49 
224.00 
219.51 

+215.03 
210.54 
206.06 
201.58 
197.09 

+192.61 



DiflF. 



-8.78 
8.68 
8*88 
8.08 
8.06 
4.01 
4.0ft 
4.08 
4.13 

4.15 

-4.18 
4.90 
4.33 
4.36 
4.38 
4*80 
4*33 
4.84 
4.SA 

4*87 

-4.88 
4.40 
4.41 
4.43 
4.43 
4.48 
4.45 
4*45 
4.46 

4.441 

-4.47 
4*48 
4.47 
4.48 
4*48 
4.40 
4*48 
4*40 
4.49 

4.48 

-4.40 
4.48 
4*48 
4.49 

-4.48 



^1 



+ 10.39 
16.00 
21.51 
26.90 
32.19 
37.37 
42.45 
47.43 
52.30 
67.07 

+ 61.74 
66.32 
70.79 
75.18 
79.46 
83.66 
87.76 
91.78 
95.70 
99.54 

+103.30 
106.97 
110.55 
114.06 
117.48 
120.83 
124.10 
127.29 
130.41 
133.45 

+136.42 
139.32 
142.14 
144.90 
147.60 
150.22 
152.78 
155.27 
157.70 
160.07 

+162.37 
164.62 
166.80 
168.92 
170.99 

+173.00 



Diff. 


& 


Diff. 


Arg. 




+68.09 





135 


+6.61 


68.65 


+0.66 


136 


ft«51 


69.20 


0*66 


137 


6.39 


69.72 


0*68 


138 


6.99 


70.23 


0.60 


139 


6.18 


70.71 


0*48 


140 


6*06 


71.18 


0.47 


141 


4*98 


71.63 


0.46 


142 


4.87 


72.07 


0.44 


143 


4.n 


72.49 


0.43 


144 


4.67 




0.40 






+72.89 




145 


+4*68 




+0.88 






73.27 




146 


4.47 


73.63 


0-36 


147 


4*89 


73.98 


0*86 


148 


4.3^ 


74.31 


0.33 


149 


4.30 


74.62 


0*81 


150 


4.10 


74.92 


0*30 


151 


4.03 


75.19 


0.37 


152 


8.93 


75.45 


0.36 


153 


8.84 


75.70 


0.36 


154 


3.76 




0.39 






+75.92 




155 


+3.67 


76.13 


+0.31 


156 


8.68 


76.32 


0*19 


157 


3.61 


76.50 


0.18 


158 


3.43 


76.66 


0.16 


159 


3.36 


76.80 


0*14 


160 


3.97 


76.93 


0.13 


161 


3.19 


77.04 


0.11 


162 


3.13 


77.13 


0.09 


163 


3.04 


77.21 


0.08 


164 


3.97 




0.06 






+77.27 




165 


+3.90 


77.32 


+0.06 


166 


9.83 


77.35 


0*03 


167 


3.76 


77.36 


+0.01 


168 


9.70 


77.36 


0.00 


169 


3.03 


77.34 


-0.09 


170 


3.66 


77.31 


0*03 


171 


9.49 


77.26 


0.06 


172 


3.48 


77.20 


0'06 


173 


9.87 


77.12 


0.08 


174 


9.30 




0.09 






+77.03 




175 


+9-96 


76.92 


-o.n 


176 


3.18 


76.80 


0.19 


177 


3*19 


76.66 


0*14 


178 


9.07 


76.51 


0.16 


179 


+9^1 


+76.34 


-0.17 


180 



ll 



+192.61 
188.14 
183.66 
179.19 
174.72 
170.25 
165.78 
161.32 
156.87 
152.41 

+147.96 
143.52 
139.07 
134.64 
130.20 
125.77 
121.34 
116.92 
112.50 
108.08 

+103.67 
99.26 
94.85 
9045 
86.05 
81.65 
77.25 
72.86 
68.47 
64.08 

+ 59.69 
55.30 
50.92 
46.53 
42.15 
37.77 
33.38 
29.00 
24.62 
20.23 

+ 15.85 

11.46 

7.08 

+ 269 

- 1.70 

- 6.09 



Diff. 



-4.47 

4>48 
4.47 
4.47 
4.47 
4*47 
4.46 
4>46 
4.46 

4.46 

-4.44 
4.46 
4.43 
4.44 

4.43 
4.43 
4.43 
4*43 
4.43 

4.41 

-4.41 
4*41 
4.40 
4*40 
4.40 
4*40 
4.39 
4.89 
4.89 



-4.89 
4.38 
4.89 

4.88 
4.88 
4.89 
4*38 
4*88 
4.89 

4*38 

-4.89 
4*88 
4.89 
4.39 

-4.89 



^l 



+173.00 

174.96 
176*86 
178.70 
180.49 
182.23 
183.92 
185.56 
187.14 
188.68 

+190.17 
191.61 
193.00 
194.34 
195*64 
196.90 
198.11 
199.28 
200.40 
201.48 

+202.52 
203.52 
204.48 
205.40 
206.28 
207.12 
207.92 
208.68 
209.40 
210.09 

+210.74 
211.35 
211.92 
212.46 
212.96 
213.42 
213.85 
214.24 
214.59 
214.91 

+215.20 
215.44 
215.65 
215.82 
215.96 

+216.06 



Diff. 


& 




+76.34 


+1.96 






76.16 


1*90 


75.96 


1.84 


75.75 


1.79 


75.53 


1*74 


75.29 


1*69 


75.03 


1*64 


74.77 


1*66 


74.49 


1*64 


74.20 


1.49 






+73.89 


+1*44 


73.57 


1.39 


73.24 


1.34 


72.89 


1.30 


72.53 


1.36 


72.16 


1*31 


71.77 


1-17 


71.38 


1*13 


70.97 


1.0R 


70.54 


1.04 






+70.11 


+1.00 


69.66 


0*96 


69.20 


0.93 


68.73 


0.88 


68.25 


0.84 


67.75 


0*80 


67.24 


0*76 


66*72 


0*73 


66*19 


0.69 


65.65 


0.65 






+65.10 


+0.61 


64.54 


0-67 


63.96 


0.64 


63.37 


0.60 


62.78 


0.46 


62.17 


0.48 


61.55 


0*39 


60.92 


C.36 


60.29 


0.33 


59.64 


0.39 






+58.98 


-H).94 


58.31 


0*31 


57.63 


0*17 


56.95 


0-14 


56.25 


-H>»10 


+55.54 



Diff. 



-0.18 
0.90 
0.31 
0.93 
0*34 
0.36 
0.96 
0.98 
0.99 

0*31 

-0*39 
0*33 
0*86 
0*36 
0*87 
0*89 
0.89 
0*41 
0.43 

0.48 

-0.46 
0*46 
0*47 
0*48 
0*60 
0*61 
0.69 
0*63 
0*64 

0.66 

-0*66 
0*68 
0*69 
0*69 
0-61 
0*69 
0*63 
0*63 
0*66 

0*66 

-0*67 
0*68 
0*68 
0*70 

-0*71 



42 



TABLE lY. —Omtinued. 

PERTURBATIONS OF THE CO-ORDINATES IN UNITS OP THE SIXTH DECIMAL. 

Terms multiplied with t Argument = M, 



Aig. 



& 



180 
181 
182 
183 
134 
185 
186 
187 
188 
189 

190 
191 
192 
193 
194 
195 
196 
197 
198 
199 

200 
201 
202 
203 
204 
205 
206 
207 
208 
209 

210 
211 
212 
213 
214 
215 
216 
217 
218 
219 

220 
221 
222 
223 
224 



' 6.09 
10.48 
14.88 
19.27 
23.67 
28.07 
32.48 
36.88 
41.29 
45.71 

- 50.13 
54.55 
58.97 
63.40 
67.84 
72.28 
76.72 
81.17 
85.63 
90.09 

- 94.55 
99.02 

103.50 
107.98 
112.47 
116.97 
121.47 
125.98 
130.49 
135.01 

-139.54 
144.07 
148.61 
153.16 
157.71 
162.27 
166.83 
171.41 
175.98 
180.56 

-185.15 

189.74 
194.34 
198.94 
203.55 
-208.16 



Diff. 



-4'89 
4>40 
4>39 
4.40 
4*40 
4*41 
4.40 
4*41 
4.43 

4*43 

-4*43 
4.43 
4*48 
4-44 
4*44 
4.44 
4.45 
4.46 
4.46 

4.46 

-4.47 
4.48 
4.48 
4.49 
4.60 
4.60 
4.61 
4.61 
4*63 

4.6S 

-4.68 
4.54 
4.65 
4*65 
4.66 
4*66 
4*58 
4.67 
4.68 

4.59 

-4.6O 
4.6O 
4.6O 
4.6I 

-4 .61 



^l 



+216.06 

216.12 
216.15 
216.13 
216.09 
216.00 
215.88 
215.72 
215.52 
215.29 

+215.02 
214.71 
214.37 
213.99 
213.57 
213.11 
212.61 
212.07 
211.49 
210.87 

+210.20 
209.50 
208.75 
207.95 
207.10 
206.21 
205.28 
204.30 
203.28 
202.20 

+201.08 
199.91 
198.70 
197.43 
196.12 
194.75 
193.34 
191.87 
190.35 
188.79 

+187.16 
185.49 
183.76 
181.98 
180.14 

+178.25 



Diff. 


ii 


Diff. 


Aig. 




455.54 






225 


+0.06 


54.82 


-0.73 


226 


+0.03 


54.10 


0.73 


227 


-0.03 


53.36 


0.74 


228 


0.04 


52.62 


0.74 


229 


0>00 


51.86 


0.76 


230 


0.13 


51.10 


0.76 


231 


0'16 


50..33 


0.77 


232 


O'SO 


49.55 


0.78 


233 


0.33 


48.77 


0-78 


234 


0.37 




0.80 






+47.97 




235 


-0.81 


47.17 


-0.80 


236 


0.84 


46.36 


0*81 


237 


0*38 


45.54 


0.83 


238 


0.43 


44.71 


0'83 


239 


0.16 


43.87 


084 


240 


0.60 


43.03 


0.84 


241 


0.64 


42.18 


0*86 


242 


0'68 


41.32 


0.86 


243 


0.G3 


40.46 


0.86 


244 


0.67 




0.67 






+39.59 




245 


-0.70 


38.71 


-0.88 


246 


0.75 


37.82 


0.89 


247 


0.80 


36.93 


0.89 


248 


0.86 


36.03 


0.90 


249 


0.89 


35.13 


0.90 


250 


0.d8 


34.22 


0.91 


251 


0.96 


33.30 


0*93 


252 


1.03 


32.38 


0.93 


253 


1*08 


31.45 


0.93 


254 


1*13 




0.98 






+30.52 




255 


-1.17 


29.58 


-0.94 


256 


1.31 


28.63 


0.96 


257 


1.37 


27.68 


0.96 


258 


1.81 


26.73 


0.96 


259 


1.87 


25.77 


0.06 


260 


1.41 


24.81 


0'96 


261 


1.47 


23.84 


0.97 


262 


1.63 


22.87 


0.97 


263 


1.56 


21.89 


0*98 


264 


1.C3 




0*98 






+20.91 




265 


-1.67 


19.92 


-0.99 


266 


1>78 


18.93 


0*99 


267 


1.78 


17.94 


0.99 


268 


1.84 


16.94 


1.00 


269 


-1.80 


+15.94 


-1.00 


270 



-208.16 
212.78 
217.40 
222.02 
226.64 
231.27 
235.00 
240.53 
245.16 
249.79 

-254.42 
259.05 
263.67 
268.30. 
272.92 
277.54 
282.16 
286.77 
291.37 
295.96 

-300.55 
305.13 
309.70 
314.25 
318.79 
323.32 
327.83 
332.33 
336.81 
341.27 

-345.71 
350.12 
354.51 
358.88 
363.2] 
367.51 
371.79 
376.03 
380.23 
384.39 

-388.51 
392.59 
396.62 
400.60 
404.53 

-408.40 



Diff. 



-4.63 
4.63 
4.68 
4*63 
4.68 
4.68 
4.68 
4.68 
4*68 

4*08 

-4.68 
4.63 
4.68 
4.63 
4*63 
4.63 
4.6I 
4. 60 
4.59 

4*69 

-4.58 
4.57 
4.55 
4.54 

4.58 
4.51 
4.50 
4.46 
4.46 

4.44 

-4.41 
4.89 
4.37 
4.38 
4.30 
4*38 
4.34 
4*30 
4.U} 

4*13 

-4.08 
4.O8 
8.96 
8.93 

-3.87 



^1 



+178.25 
176.30 
174.29 
172.23 
170.11 
167.92 
165.68 
163.37 
160.99 
158.55 

+156.04 
153.46 
150.80 
148.08 
145.28 
142.40 
139.44 
136.40 
133.28 
130.08 

+126.80 
123.44 
119.99 
116.45 
112.83 
109.12 
105.32 
101.43 
97.45 
93.38 

+ 89.22 
84.96 
80.60 
76.14 
71.58 
66.92 
62.16 
57.29 
52.32 
47.24 

+ 42.05 
36.75 
31.34 
25.82 
20.18 

+ 14.43 



Diff. 


(l 




+15.94 


-1.96 


14.94 


3.01 


13.94 


3.06 


12.93 


3.13 


11.92 


3-19 


10.91 


334 


9.90 


3.81 


8.88 


3.88 


7.86 


3.46 


6.84 


3.51 


• 




+ 5.82 


-3.68 


4.80 


366 


3.78 


3.73 


2.76 


3.EO 


1.73 


3*88 


+ 0.71 


3.96 


- 0.31 


804 


1.34 


8.19 


2.36 


3-SO 


3.39 


8.38 






- 4.41 


-3.36 


5.43 


845 


6.45 


8.M 


7.47 


363 


8.49 


8.71 


9.51 


880 


10.52 


8.89 


11.53 


8-98 


12.54 


4.07 


13.55 


4*16 






-14.55 


-4.36 


15.55 


4.86 


16.54 


4.46 


17.54 


4.56 


18.52 


4.66 


19.51 


4.76 


20.49 


4.87 


21.46 


4.97 


22.43 


5.O8 


23.39 


6.19 






-24.35 


-5.8O 


25.30 


6.41 


26.24 


5.53 


27.18 


5.64 


28.11 


-5.75 


-29.03 



Diff. 



-1.00 

I'OO 
1*01 

1.01 
1.01 

1<01 
1*03 
1-03 
1.03 

1<03 

-103 
103 
1-03 
1.08 
1-03 
1-03 
1*03 
1*03 
1.08 

1.03 

-1 03 
1.03 
1*03 
1.03 
1 03 
1-01 
1*01 
1-01 
1 01 

100 

-l^X) 
0.99 
1-M 
0.98 
0.99 
0.98 
0*97 
0.97 
0.96 

0.96 

-000 
0.94 
0*94 
0.98 

-0*93 



43 



TABLE lY :—Caniinued. 

PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. 

Terms mnltiptied with t. Argnment = M. 



Arg. 



270 
271 
272 
273 
274 
275 
276 
277 
278 
279 

280 
281 
282 

283 
284 
285 
286 

287 
288 
289 

290 
291 
292 
293 
294 
295 
296 
297 
298 
299 

300 
301 
302 
303 
304 
305 
306 
307 
308 
309 

310 
311 
312 
313 
314 
315 



& 



-408.40 
412.21 
415.97 
419.65 
423.27 
426.82 
430.29 
433.68 
436.99 
440.21 

-443.34 
446.38 
449.32 
452.15 
454.87 
457.49 
459.98 
462.36 
464.60 
466.72 

-468.70 
470.54 
472.23 
473.76 
475.14 
476.36 
477.40 
478.27 
478.96 
479.46 

-479.78 
479.90 
479.81 
479.52 
479.00 
478.27 
477.30 
476.10 
474.65 
472.96 

-471.01 
463.79 
466.32 
463.57 
460.55 

-457.24 



Diff. 



-8.81 
8-76 
3.68 
8.63 
8>6ft 
8*47 
8.86 
8>81 
8.33 

8.18 

-3.04 
3-94 
3.88 
3.73 
3.63 
3-49 
3.38 
3.34 
3.13 

1.98 

-1.84 
1.69 
1.53 
1.88 
r.33 

*1^W 
0-87 
0.69 
0.S0 

0*83 

-0.13 
+0.09 
0.39 
0*53 
0.78 
0-97 
1*30 
1*45 
1.69 

1.95 

+3-33 
3.47 
3.75 
8.03 

+8.31 



^l 



+ 14.43 

8.56 

+ 2.57 

- 3.54 
9.77 

16.11 
22.58 
29.18 
35.89 
42.73 

- 49.69 
56.78 
63.99 
71.33 
78.80 
86.39 
94.10 

101.94 
109.90 
117.99 

-126.20 
134.53 
142.98 
151.55 
160.24 
169.05 
177.97 
187.01 
196.16 
205.42 

-214.78 
224.25 
233.82 
243.48 
253.24 
263.09 
273.02 
283.02 
293.10 
303.26 

-313.48 
323.75 
334.08 
344.46 
354.88 

-365.32 



Diff. 


& 


Diff. 


Arg. 




-29.03 






315 


- 5.87 


29.95 


-0.93 


316 


5.99 


30.86 


0.91 


317 


6.11 


31.76 


0.90 


318 


6.38 


32.65 


0-89 


319 


6.34 


33.53 


0.88 


320 


6.47 


34.40 


0.87 


321 


6.60 


35.26 


0*86 


322 


6.71 


36.12 


0*88 


323 


6.84 


36.96 


0*84 


324 


6.96 




0*83 






-37.79 




325 


- 7.09 


38.61 


-0.83 


326 


7.31 


39.41 


0.E0 


327 


7*34 


40.21 


0.80 


328 


7.47 


40.99 


0.78 


329 


7.59 


41.76 


0.77 


330 


7.71 


42.52 


0.76 


331 


7.84 


43.26 


0.74 


332 


7*96 


43.99 


0.73 


333 


8.09 


44.71 


0*73 


334 


8.31 




0*70 






-45.41 




335 


- 8-33 


46.10 


-0*69 


336 


8*45 


46.77 


0*67 


337 


8.57 


47.42 


0*65 


338 


8.69 


48.06 


64 


339 


8.81 


48.68 


0*03 


340 


8.93 


49.29 


0*61 


341 


9.04 


49.87 


0*58 


342 


9.15 


50.44 


0*57 


343 


9*36 


50.99 


0*55 


344 


9.36 




0*53 






-51.52 




345 


- 9.47 


52.03 


-0.61 


346 


9.57 


52.52 


0*49 


347 


9.6G 


52.99 


0*47 


348 


9.76 


53.44 


0.45 


349 


9.85 


53.87 


0*43 


350 


9.98 


54.28 


0*41 


351 


10.00 


54.67 


0*39 


352 


10*08 


55.03 


0.36 


353 


10*16 


65.37 


0*34 


354 


10*33 




0*33 






-55.69 




355 


-10*37 


55.99 


-0.80 


356 


10*88 


56.26 


- 0.37 


357 


10.86 


56.50 


0.34 


358 


10.43 


56.72 
-56.92 


0*33 


359 


-10.44 


-0*30 


360 



-457.24 
453.65 
449.75 
445.57 
441.07 
436.26 
431.15 
425.71 
419.95 
413.87 

-407.46 
400.72 
393.66 
386.26 
378.53 
370.48 
362.10 
353.39 
344.36 
335.01 

-325.34 
315.35 
305.03 
294.42 
283.51 
272.30 
260.82 
249.07 
237.06 
224.81 

-212.31 
199.59 
186.65 
173.50 
160.15 
146.64 
132.95 
119.11 
105.16 
91.08 

- 76.91 
62.67 
48.36 
34.01 
19.63 

- 5.24 



Diff 



+ 8.50 
3*90 
4. 18 
4.50 
4.8I 
5*11 
5*44 
5*76 
6*08 

6*41 

+ 6*74 
7*06 
7*40 
7*73 
8*05 
8-38 
8*71 
9*03 
9*35 

9*07 

+ 9.99 
.0*33 
0-61 
0*91 
1-31 
1*48 
1*75 
3*01 
2.35 

3*50 

3.73 
3.94 
3.15 
3*35 
3*51 
3*69 
3*84 
3*95 
4*08 

4*17 

4.34 
4.8I 
1*35 
4.38 
8*39 



Vl 



-365.32 

375.78 
386.26 
396.75 
407.22 
417.67 
428.09 
438.48 
448.82 
459.11 

-469.34 
479.48 
489.53 
499.48 
509.30 
519.00 
528.54 
537.91 
547.12 
556.14 

-564.95 
573.56 
581.93 
590.06 
597.95 
605.56 
612.89 
619.93 
626.66 
633.06 

-639.14 
644.88 
650.26 
655.28 
659.91 
664.16 
668.02 
671.48 
674.53 
677.18 

-679.42 
681.24 
682.63 
683.60 
684.12 

-«S4.22 



Diff. 


(l 




-56.92 


-10.46 


57.09 


10.48 


57.23 


10*49 


57.35 


10.47 


57*44 


10*45 


57.50 


10*43 


57.54 


10*89 


57.55 


10*34 


57.53 


10*39 


57.48 


10*38 






-57.40 


-10*14 


57.29 


1005 


57.15 


9*95 


56.98 


9*83 


56.78 


9*70 


56.55 


9*54 


56.29 


9.87 


56.00 


9*31 


55.68 


9*03 


55.33 


8*81 






-54.95 


- 8*61 


54.54 


8 37 


54.10 


8*13 


53.62 


7*89 


53.12 


7.6I 


52.58 


7*33 


52.01 


7.04 


51.42 


6.73 


50.79 


6.40 


50.13 


6.08 






-49.44 


• 5*74 


48.72 


5*38 


47.97 


6.03 


47.19 


4*63 


46.39 


4*35 


45.55 


8*86 


44.69 


8.46 


43.79 


8*05 


42.87 


3.65 


41.93 


3.34 






-40.95 


• 1.83 


39.95 


1*89 


38.93 


0*97 


37.88 


0*53 


36.81 


■ 0*10 


-35.71 



Diff 



-0.17 
0*14 
0*13 
009 
0*06 
0*04 
^0*01 
+0*03 
0*05 

0.08 

+0*11 
0*14 
0.17 
0*30 
0*38 
0.36 
0.30 
0.33 
0*35 

0*38 

+0.41 
0*44 
0*48 
0*50 
0*54 
0.57 
0*59 
0.68 
0.66 

0*69 

+0*73 
0*75 
0.78 
0*80 
0*84 
0*86 
0*90 
0.93 
0*94 

0*98 

+1*00 
1*03 
1*05 
1*07 

+1.10 



44 





TABLE lY.—Coniimed 


i 


PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. | 




ARGUMENT I. 


1 


Aig. 


6 


Diff. 


ni 


Diff. 


il 


Diff. 


Arg. 


6 


Diff. 


Vl 


Diff. 


(l 


Diff. 


o 



-577 


. 


+177 




+21 




o 
45 


+ 303 




+928 




+37 




1 


570 


+ 7 


201 


+34 


21 





46 


339 


+86 


933 


+ 6 


38 


+1 


2 


562 


8 


225 


34 


21 





47 


375 


36 


936 


8 


38 





3 


554 


8 


248 


38 


22 


+1 


48 


412 


87 


938 ' 


3 
+ 3 


39 


1 


4 


545 


9 


271 


38 


22 





49 


450 


38 


940 


40 


1 

• 


5 


536 


9 


294 


38 


22 





50 


488 


88 


939 


- 1 


41 


1 


6 


526 


10 


316 


33 


22 





51 


527 


89 


938 


1 


41 





7 


515 


11 


338 


33 


23 


1 


52 


567 


40 


935 


8 


42 


1 


8 


504 


11 


360 


33 


23 





53 


607 


40 


930 


6 


43 


1 

m 


9 


493 


11 
13 


381 


31 
31 


23 






54 


648 


41 

41 


925 


6 
8 


44 


1 

I 


10 


-481 




+402 




+23 




55 


+ 689 




+917 




+45 




11 


468 


+13 


423 


+31 


24 


+1 


56 


731 


+43 


908 


- 9 


46 


+1 


12 


455 


13 


444 


31 


24 





57 


773 


43 


898 


10 


46 





13 


441 


14 


464 


30 


24 





58 


815 


43 


885 


13 


47 


1 


14 


427 


14 


484 


30 


24 





59 


857 


43 


871 


14 


48 


1 


15 


413 


14 


503 


19 


24 





60 


900 


48 


856 


16 


49 


1 


16 


398 


15 


522 


19 


25 


1 


61 


942 


43 


838 


18 


50 


1 


17 


383 


15 


542 


90 


25 





62 


985 


48 


819 


19 


50 





18 


367 


16 


560 


18 


25 





63 


1027 


43 


798 


31 


51 


1 


19 


350 


17 
17 


579 


19 
18 


25 




1 


64 


1069 


. 43 
43 


775 


93 
36 


51 




1 


20 


-333 




+597 




+26 




65 


+1111 




+750 




+52 




21 


316 


+17 


615 


+18 


26 


+0 


66 


1153 


+43 


723 


-37 


52 


+0 

m 


22 


298 


18 


633 


19 


26 





67 


1194 


41 


695 


98 


53 


1 


23 


279 


19 


650 


17 


26 





68 


1234 


40 


665 


80 


53 




+1 


24 


260 


19 


667 


17 


27 


1 


69 


1274 


40 


632 


83 


54 


25 


241 


• 19 


684 


17 


27 





70' 


1314 


40 


598 


> 


54 





26 


220 


31 


701 


17 


27 





71 


1352 


88 


563 


35 


54 





27 


200 


90 


717 


16 


28 


1 


72 


1390 


38 


525 


38 


54 





28 


178 


33 


733 


16 


28 





73 


1427 


87 


485 


40 


54 





29 


156 


33 
33 


749 


16 
16 


28 




1 


74 


1463 


86 
86 


444 


41 
48 


54 




-1 


30 


-133 




+764 




+29 




75 


+1498 




+401 




+63 




31 


109 


+34 


779 


+16 


29 


+0 


76 


1532 


+34 


356 


-45 


53 


-0 


32 


85 


34 


793 


14 


29 





77 


1564 


83 


310 


46 


53 




■ 


33 


60 


35 


807 


14 


30 


1 


78 


1595 


81 


262 


48 


52 


1 


34 


34 


36 


821 


14 


30 





79 


1625 


80 


212 


50 


51 


1 


35 


- 8 


30 


834 


13 


31 


1 


80 


1653 


38 


161 


61 


51 





36 


+ 20 


38 


847 


13 


31 





81 


1680 


37 


108 


63 


50 


1 


37 


48 


38 


859 


13 


32 


1 


82 


1705 


36 


+ 54 


64- 


49 


1 


38 


77 


39 


870 


11 


32 





83 


1729 


34 


- 2 


66 


47 


3 


39 


107 


80 
80 


881 


11 
10 


33 


1 




84 


1751 


93 

30 


59 


57 
60 


46 


1 
1 


40 


+137 




+891 




+33 




85 


+1771 




-118 




+45 




41 


169 


+33 


900 


+ 


34 


+1 


86 


1789 


+18 


178 


-60 


43 


-9 


42 


201 


33 


908 


8 


35 


1 


87 


1805 


16 


239 


61 


41 


3 

m 


43 


234 


88 


916 


8 


35 





88 


1819 


14 


301 


63 


40 


1 


44 


268 


34 


923 


7 


36 


1 


89 


1831 


13 


365 


64 


38 


3 


45 


+303 


+85 


+928 


+ 6 


+37 


+1 


90 


+1841 


+10 


-429 


-64 


+36 


-9 



45 











TABLE lY.—Coniinued 












PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. 










ARGUMENT I. 












Arg. 


& 


Diff. 


Vl 


Diff. 


il 


Diff. 


Arg. 


h 


Diff. 


Vl 


Diff. 


bl 


Diff 


o 

90 
91 


+1841 

1848 


+ 7 


-429 
495 


-66 


+ 36 
34 


-9 



135 

136 


- 408 
506 


-98 


-2839' 
2840 


- 1 

t ^ 


-116 
119 


-3 


92 


1854 


6 
+ 3* 


- 1 


561 


66 


31 


8 


137 


605 


99 


2637 


+ 3 


122 


3 


93 
94 
95 


1857 
1857 
1856 


628 
696 
765 


67 
68 
69 


29 
27 
24 


3 
3 
8 


138 
139 
140 


704 
803 
902 


99 
99 
99 


2831 
2820 
2806 


6 
11 
14 


125 
127 
130 


3 
3 
3 


96 


1851 


5 


834 


69 


21 


8 


141 


1001 


99 


2788 


16 


132 


3 


97 
98 


1844 
1835 


7 
9 


904 
975 


70 
71 


18 
15 


8 
8 


142 
143 


1100 
1198 


99 
98 


2767 
2741 


31 
36 


134 
136 


3 
3 


99 


1823 


13 
15 


1045 


70 
71 


12 


8 
8 


144 


1295 


97 
90 


2712 


39 
38 


138 


3 

3 


100 
101 


+1808 
1791 


-17 


-1116 
1187 


-71 


+ 9 
6 


—8 


145 
146 


-1391 

1487 


-96 


-2679 
2642 


+ 37 


-140 
141 


-1 


102 


1771 


90 


1259 


73 


+ 3 




147 


1581 


94 


2602 


40 


143 


3 


103 


1748 


33 


1330 


71 







148 


1674 


93 


2558 


44 


144 




104 


1722 


36 


1401 


71 


- 4 




149 


1766 


93 


2510 


48 


145 




105 


1693 


39 


1471 


70 


7 




150 


1856 


90 


2459 


51 


146 




106 


1661 


82 


1542 


71 


11 




151 


1944 


88 


2405 


54 


147 




107 


1626 


85 


1612 


70 


14 




152 


2030 


86 


2347 


58 


148 




108 
109 


1589 
1548 


87 
41 

44 


1681 
1749 


69 
68 

68 


18 
22 




153 
154 


2114 
2196 


84 
83 

80 


2286 
2221 


61 
65 

67 


148 
149 



-1 




110 
111 


+1504 
1458 


-46 


-1817 
1883 


-66 


- 25 
29 


• 


155 
156 


-2276 
2354 


-78 


-2154 

2083 


+ 71 ' 


-149 
149 





112 


1409 


49 


1949 


66 


33 




157 


2429 


75 


2009 


74 


149 




t - 


113 
114 


1356 
1301 


53 
55 


2013 
2075 


64 
63 


37 
41 




158 
159 


2501 
2571 


73 
70 


1933 
1854 


76 
79 


148 
148 


+1 



115 


1243 


58 


2136 


61 


45 




160 


2637 


66 


1772 


83 


147 




116 


1182 


61 


2196 


60 


48 




161 


2701 


64 


1668 


84 


146 




117 


1118 


64 


2253 


57 


52 




162 


2762 


61 


1601 


87 


145 




118 


1052 


66 


2309 


56 


56 




163 


2819 


57 


1512 


89 


144 




119 


983 


69 
73 


2363 


54 
51 


60 




164 


2874 


55 
51 


1420 


93 
98 


143 


3 


120 
121 


+ 911 
837 


-74 

0mtm 


-2414 
2463 


-49 


-64 
68 


—4 


165 
166 


-2925 
2973 


-48 


-1327 
1232 


+ 95 


-141 
140 


+1 


122 


760 


77 


2509 


46 


72 




167 


3017 


44 


1135 


97 


138 


3 


123 


681 


79 


^53 


44 


75 




168 


3058 


41 


1036 


09 


136 


3 


124 


600 


81 


2595 


43 


79 




169 


3095 


87 


935 


101 


134 


3 


125 


516 


81 


2633 


88 


83 




170 


3128 


33 


833 


103 


132 


3 


126 

* 127 


431 
344 


8) 
87 


2668 
2701 


85 
33 


86 
90 




171 
172 


3158 
3184 


80 

36 


730 
626 


1C3 
104 


129 
127 


8 
3 


128 


255 


69 


2730 


39 


94 




173 


3206 


33 


521 


105 


124 


8 


129 


164 


91 
93 


2756 


36 
33 


97 


3 
3 


174 


3224 


18 
15 


414 


107 
107 


121 


8 
8 


130 
131 
132 
133 
134 
135 


+ 71 

- 22 

117 
213 
310 

- 408 


-93 
95 
96 
97 

-98 


-2778 
2797 
2813 
2825 
2834 

-2839 


-19 

16 

13 

9 

- 5 


-100 
104 
107 
110 
113 

-116 


-4 

8 

8 

8 

-8 


175 
176 
177 
178 
179 
180 


-3239 
3249 
3255 
3258 
3256 

-3251 


,-10 

- 3 

+ 9 
+ 5 


- 307 
200 

- 92 
+ 17 

125 
+ 234 


+107 
106 
109 
106 

+109 


-118 
115 
112 
109 
105 

-102 


+8 
8 
3 
4 

+8 



46 











TABLE IV.— CbwfewtteJ. 










PERTURBATIONS OP THE CO-ORDINATES IN UNITS OF THE SDITH DECIMAL. | 










ARGUMENT I. 






/ 




Aig. 


& 


Diff. 


^1 


Diff. 


ii 


Diff. 


Arg. 


6 


Diff. 


Vl 


Diff. 


ii 


Diff. 


o 
180 

181 


-3251 
3241 


« 
+ 10 


+ 234 
342 


+108 


-102 
98 


+4 


o 

225 

226 


+ 122 

220 


+98 


+2878 
2857 


-31 


+78 
80 


+3 


182 


3228 


13 


450 


106 


94 




227 


316 


96 


2832 


36 


82 


3 


183 


3210 


18 


558 


108 


91 




228 


411 


96 


2804 


38 


84 


3 


184 


3188 


33 


664 


106 


87 




229 


505 


94 


2773 


81 


86 


3 


185 


3163 


35 


771 


107 


83 




230 


596 


91 


2738 


85 


88 


3 


186 


3133 


80 


876 


106 


79 




231 


686 


90 


2700 


38 


90 


3 


187 

188 


3099 
3062 


84 
87 


980 
1083 


104 
108 


75 

70 




232 
233 


774 
859 


88 
85 


2659 
2615 


41 
44 


92. 
93 


3 


189 


3020 


43 


1184 


101 
100 


66 




234 


942 


63 
81 


2568 


47 
60 


94 




190 
191 


-2975 
2926 


+ 49 


+1284 
1382 


+ 06 


-62 
57 


+6 


235 
236 


+1023 
1101 


+78 


+2518 
2466 


-53 


+95 
96 


+1 


192 


2874 


ft3 


1478 


96 


53 




237 


1177 


76 


2411 


66 


. 97 




193 


2817 


67 


1572 


94 


49 




238 


1250 


78 


2354 


67 


98 




194 


2758 


89 


1664 


93 


44 




239 


1320 


70 


2294 


60 


98 




195 


2695 


63 


1754 


90 


40 




240 


1388 


66 


2233 


61 


98 




196 
197 
198 


2628 
2558 
2485 


70 
78 


1841 
1926 
2008 


67 
86 
83 


35 
3] 
26 




241 
242 
243 


1453 
1514 
1573 


66 
61 

60 


2169 
2103 
2036 


64 
66 
67 


98 
99 
98 


+1 


199 


2410 


76 
79 


2087 


79 
76 


22 




244 


1629 


66 
63 


1967 


69 
71 


98 




200 
201 

202 


-2331 
2249 
2165 


+ 83 
84 


+2163 

2236 

'2306 


+ 78 
70 


- 17 
13 

8 


+4 


245 
246 
247 


+1662 
1732 

1778 


+50 
46 


+1696 
1824 
1751 


-73 
73 


+98 
97 
97 


— 1 


203 
204 


2079 
1990 


68 
89 


2372 
2435 


66 
68 


- 4 

+ 1 




248 
249 


1822 
1862 


44 

40 


1676 
1601 


76 
75 


96 
95 




205 


1899 


91 


2495 


60 


5 




250 


1899 


87 


1524 


77 


94 




206 


1806 


98 


2551 


66 


10 




251 


1933 


84 


1447 


77 


93 




207 


1711 


96 


2603 


63 


14 




252 


1963 


80 


1369 


78 


92 




208 


1614 


97 


2651 


48 


18 




253 


1990 


37 


1291 


78 


90 




209 


1516 


98 
99 


2696 


46 

41 


23 




254 


2015 


36 
30 


1212 


79 

78 


89 


A 


210 
211 


-1417 
1316 


+101 


+2737 
2774 


+ 87 


+ 27 
31 


+4 


255 
256 


+2035 
2053 


+18 


+1134 
1055 


-79 


+87 
86 


—1 


212 


1214 


103 


2807 


88 


35 




257 


2067 


14 


976 


79 


84 




213 


1112 


103 


2836 


39 


39 




258 


2079 


13 


897 


79 


82 




214 


1008 


104 


2861 


36 


43 




259 


2087 


8 


818 


79 


80 




215 


905 


108 


2882 


31 


46 




260 


2093 


6 

1 4« 


740 


78 


78 




216 
217 


801 
697 


104 
104 


2900 
2913 


18 
18 


50 
54 




261 
262 


2095 
2094 


+ 3 
- 1 


663 
586 


77 
77 


76 

74 


Q • 


218 


593 


104 


2922 


9 


57 




263 


2090 


4 


509 


77 


72 




219 


489 


104 
104 


2927 


6 
+ 3 


60 




264 


2083 


7 
9 


434 


76 

74 


70 




220 
221 


- 385 
282 


+108 


+2929 
2926 


- 8 


+ 63 
67 


+4 


265 
266 


+2074 
2061 


-13 


+ 360 
286 


-74 


+68 
66 


-3 


222 


180 


103 


2920 


6 


70 




267 


2046 


16 


214 


73 


63 




223 
224 
225 


- 78 
+ 22 
+ 122 


103 

100 

+M0 


2910 

2896 

+2878 


10 

14 

- 18 


72 

75 

+ 78 


+3 


268 
269 
270 


2029 

2008 

+1985 


31 

-33 


143 

74 
+ 6 


71 

69 

-68 


61 

59 

+56 


3 
-8 



1 



47 



TABLE lY .^CkmtinuecL 

PERTURBATIONS OP THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. 

ARGUMENT I. 



Aig. 



270 
271 
272 
273 
274 
275 
276 
277 
278 
279 

230 
231 
282 
283 
284 
285 
236 
287 
238 
289 

290 
291 
292 

293 
294 
295 

296 
297 

298 
299 

300 
301 
302 
303 
304 
305 
306 
307 
308 
309 

310 
311 
312 
313 
314 
315 



+1985 
1960 
1933 
1903 
1871 
1837 
1802 
1764 
1725 
1684 

+1641 
1597 
1552 
1505 
1458 
1409 
1360 
1310 
1259 
1208 

+1156 
1104 
1052 
999 
947 
895 
843 
791 
740 
689 

+ 638 
588 
539 
490 
443 
396 
350 
304 
260 
217 

+ 175 

134 

94 

55 

+ 17 

- 20 



Diff. 



-35 
37 
80 
83 
84 
3S 
88 
89 
41 

48 

-44 
49 
47 
47 
49 
49 
fiO 
61 
51 

53 

-53 
53 
58 
53 
53 
53 
53 
51 
51 

51 

-50 
49 
49 
47 
47 
46 
46 
44 
48 

43 

-41 
40 
89 
88 

-87 



n\ 



+ 6 

- 61 

126 
189 
250 
309 
367 
422 
475 
527 

- B76 
623 
668 
710 
750 
788 
824 
857 
888 
916 

--942 
966 
968 
1008 
1025 
1040 
1053 
1064 
1072 
1079 

-1084 
1087 
1088 
1087 
1085 
1081 
1075 
1068 
1059 
1049 

-1037 

1024 

1010 

995 

979 

- 962 



Diff. 



-67 
65 
68 
61 
59 
58 
55 
58 
53 

49 

-47 
45 
43 
40 
88 
86 
83 
81 
38 

36 

-34 
33 
30 
17 
15 
18 
11 
8 
7 



- 8 

- 1 

+ 1 
3 
4 
6 
7 
9 
10 

13 

+18 
14 
15 
16 

+17 



+56 
54 
51 
49 
46 
44 
42 
39 
37 
34 

+32 
30 
27 
25 
23 
21 
18 
16 
14 
12 

+10 
8 
7 
5 
3 

+ 2 


- 1 
2 
4 

-5 
6 

7 

7 

8 

9 

9 

10 

10 

10 

-10 

10 
10 
10 
10 
-10 



Diff. 



-3 
8 
3 
8 
3 
3 
8 
3 
8 



~2 
8 
3 
3 
3 
8 
3 
3 
3 



-3 
1 
3 
3 
1 
3 
1 
1 
3 



-1 
1 

1 
1 

■1 













Arg. 



315 
316 
317 
318 
319 
320 
321 
322 
323 
324 

325 
326 
327 
328 
329 
330 
331 
332 
333 
334 

335 
336 
337 
338 
339 
340 
341 
342 
343 
344 

345 
346 
347 
348 
349 
350 
351 
352 
353 
354 

355 
356 
357 
358 
359 
360 



- 20 
55 
89 
122 
154 
185 
215 
243 
270 
296 

-321 
345 
368 
390 
410 
430 
448 
465 
481 
497 

--611 
524 
536 
548 
558 
567 
576 
583 
590 
595 

-600 
604 
607 
609 
611 
611 
611 
610 
609 
606 

-603 
599 
595 
590 

584 
-677 



Diff. 



-85 
84 
88 
83 
81 
80 
38 
37 
36 

35 

-34 
S3 
33 
SO 
30 
18 
17 
16 
16 

14 

-18 

13 

13 

10 

9 

9 

7 

7 

6 

5 

- 4 
8 
3 

- 3 



+ 1 
1 
8 



+ 4 

4 

5 

G 

+ 7 



Vi 



-962 • 
944 
925 
905 
884 
863 
841 
818 
795 
771 

-747 
722 
697 
671 
645 
619 
593 
566 
539 
512 

-485 
458 
431 
403 
376 
348 
321 
293 
266 
239 

-211 

184 

157 

130 

.103 

77 

50 

- 24 

+ 2 

28 

+ 53 

79 

104 

129 

153 

+177 



Diff. 



+18 
19 
30 
31 
31 
33 
S3 
38 
34 

34 

+35 
35 
36 
36 
36 
36 
37 
37 
37 

37 

+37 
27 
38 
37 
38 
37 
38 
37 
27 

38 

+37 
37 
37 
37 
36 
37 
36 
36 
36 

35 

+26 
35 
35 
34 

+34 



-10 
9 
9 
8 
8 
7 
6 
6 
5 
4 

- 3 
2 
1 

- 1 


+ 1 
2 
3 
4 
5 

+ 6 

7 

8 

8 

9 

10 

11 

12 

12 

13 

+14 
14 
15 
16 
16 
17 
17 
18 
18 
19 

+19 
19 
20 
20 
20 

+21 



Dar. 



+1 



1 



1 
1 



1 

1 

1 

+1 

1 



1 
1 
1 
1 
1 
1 

1 

+1 

1 



1 
1 
1 
1 



1 



+0 

1 
1 



1 



1 



1 



+0 

1 




+1 



48 



TABLE lY.—Caniinued. 

PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. 

ARGUMENT H. 



Aig. 




1 
2 
3 
4 
5 
6 
7 
8 
9 

10 
11 
12 
13 
14 
15 
16 
17 
18 
19 

20 
21 
22 
23 
24 
25 
26 
27 
28 
29 

30 
31 
32 
33 
34 
35 
36 
37 
38 
39 

40 
41 
42 
43 
44 
45 



+551 
550 
548 
547 
546 
544 
542 
540 
538 
536 

+534 
531 
528 
525 
521 
517 
513 
508 
503 
498 

+492 
485 
478 
470 
462 
453 
444 
434 
423 
411 

+399 
386 
372 
358 
342 
326 
309 
291 
273 
253 

+233 
211 

189 

166 

142 

+118 



Diff. 



- 1 

3 
1 
1 
3 
3 
3 
3 
3 



- 8 
8 
3 
4 

4 
4 
6 
fi 
5 

6 

- 7 
7 
8 
8 
9 


10 
11 
13 

13 

-18 
14 
14 
16 
16 
17 
18 
18 
90 

30 

-33 
33 
38 

34 
-34 



m 



+ 51 

65 

78 

91 

105 

118 

134 

146 

160 

174 

+188 
202 
217 
231 
246 
261 
276 
292 
307 
323 

+339 
355 
371 
387 
404 
420 
437 
453 
470 
487 

+503 
520 
536 
553 
569 
685 
601 
617 
632 
647 

+661 
676 
689 
703 
715 

+727 



Diff. 



Ci 



Diff. 



+14 
13 
13 
14 
IS 
14 
14 
14 
14 

14 

+14 
15 
14 
15 
15 
15 
16 
15 
16 

16 

+16 
16 
16 
17 
16 
17 
16 
17 
17 

16 

+17 
16 
17 
16 
16 
16 
16 
15 
15 

14 

+15 
18 
14 
13 

+13 



-38 
37 
37 
36 
35 
34 
34 
33 
32 
31 

-31 
30 
29 
28 
28 
27 
27 
26 
25 
25 

-24 
24 
24 
23 
23 
22 
^ 
22 
22 
22 

-21 
21 
21 
21 
21 
21 
21 
21 
21 
21 

-22 
22 
22 
22 
22 

-23 



+1 



1 
1 
1 



1 
1 
1 



+1 
1 
1 



1 



1 
1 



1 

+0 


1 



1 






Ai^. 



45 
46 
47 
48 
49 
50 
51 
52 
53 
54 

55 
56 
57 
58 
59 
60 
61 
62 
63 
64 

65 
66 
67 
68 
69 
70 
71 
72 



V 


73 





74 


+1 






75 





76 





77 





78 





79 





80 





81 





82 





83 





84 


-1 






&5 





86 





87 





88 





89 


— 1 


90 



+ 118 
92 
66 
39 

+ 12 

- 17 
46 
76 

106 
137 

- 169 
201 
233 
266 
299 
333 
367 
401 
435 
470 

- 504 
538 
573 
607 
641 
674 
708 
740 
773 
805 

- 836 
866 
896 
925 
953 
980 

1006 
1031 
1055 
1077 

-1098 
1118 
1137 
1154 
1170 

-1184 



Diff. 



-36 
36 
37 
37 
30 
39 
80 
80 
81 

S3 

-83 
83 
88 
88 
84 
84 
84 
84 
85 

84 

-84 

85 
84 
84 
88 
84 
83 
88 
83 

81 

-80 
80 
30 
36 
37 
36 
35 
34 
33 

31 

-30 
19 
17 
16 

-14 



^1 



+727 

739 
750 
760 
769 

777 
785 
791 
797 
802 

+805 
808 
810 
810 
809 
807 
804 
799 
793 
786 

+778 
768 
756 
744 
730 
714 
697 
679 
660 
638 

+616 
592 
667 
540 
512 
483 
453 
421 
388 
354 

+319 
282 
245 
206 
167 

+127 



Diff. 



+13 
11 
10 

8 
8 
6 
6 
5 

8 

+ 8 
+ 3 

- 1 
3 
8 
5 
6 
7 

8 

-10 
13 
13 
14 
16 
IT 
18 
19 
90 

S3 

-34 
35 
37 
38 
39 
80 
S3 
88 
84 

85 

-87 
37 
89 
89 

-40 



-23 
23 
23 
24 
24 
24 
24 
25 
25 
25 

-26 
26 
26 
27 
27 
27 
27 
27 
28 
28 

-28 
28 
28 
28 
28 
28 
28 
28 
27 
27 

-27 
26 
26 
26 
25 
24 
24 
23 
22 
22 

-21 
20 
19 
18 
17 

-15 



Diff. 



-0 



1 





1 






-0 


1 






-1 













+1 




+1 




1 
1 



1 
1 



1 

+1 

1 
1 
1 

+3 






49 



TABLE lY.—Cantmued. 

PERTURBATIONS OF THE COORDINATES IN UNITS OF THE SIXTH DECIMAL. 

ARGUMENT n. 



Arg. 



90 
91 
92 
93 
94 
95 
96 
97 
98 
99 

100 
101 
102 
103 
104 
105 
106 
107 
108 
109 

110 
111 
112 
113 
114 
115 
116 
117 
118 
119 

120 
121 
122 
123 
124 
125 
126 
127 
128 
129 

130 
131 
132 
133 
134 
135 



-1184 
1196 
1207 
1216 
1223 
1228 
1232 
1234 
1234 
1232 

-1228 
1222 
1214 
1204 
1193 
1179 
1163 
1146 
1126 
1104 

-1081 
1056 
1028 
999 
968 
936 
901 
865 
827 
788 

- 747 
705 
661 
616 
569 
522 
473 
423 
372 
320 

- 267 
214 
160 
105 

- 50 
+ 5 



Diff. 



-12 
11 
9 
7 
6 
4 

- 3 


+ 2 



+ 6 
8 
10 
11 
14 
16 
17 

30 
22 

28 

+25 
28 
20 
81 
82 
86 
86 
88 
80 

41 

+42 
44 

45 
47 
47 
40 
50 
51 
52 

58 

+58 
54 

55 
55 

+55 



Vl 



Diff. 



+ 127 

86 

44 

+ 1 

- 42 
85 

130 
174 
219 
265 

- 310 
356 
401 
447 
492 
538 
583 
627 
671 
715 

- 758 
800 
842 
882 
922 
961 
999 

1035 
1070 
1104 

-1137 
1168 
1197 
1225 
1252 
1277 
1300 
1321 
1340 
1357 

-1373 
1386 
1398 
1408 
1415 

-1420 



-41 
42 
48 
48 
48 
45 
44 
45 
46 

45 

-46 
45 

46 
45 
46 
45 
44 
44 
44 

48 

-42 
42 
40 
40 
89 
88 
86 
85 
84 

88 

-81 
29 
28 
27 
25 
28 
21 
19 
17 

16 

-18 
12 
10 

7 
+ 5 



-15 

14 

13 

11 

10 

9 

7 

5 

4 

-2 



+ 1 

3 

5 

7 

9 

11 

13 

15 

17 

+20 
22 
24 
26 
29 
31 
33 
35 
38 
40 

+42 
45 
47 
49 
52 
54 
56 
59 
61 
63 

+65 
67 
69 
72 
74 

+76 



Diff. 



+1 
1 

2 
1 
1 
2 
• 2 
1 
2 

2 

+1 
2 
2 
2 
2 
2 
2 
2 
2 

8 

+2 
2 
2 
8 
2 
2 
2 
8 
2 

2 

+8 
2 
2 
8 
2 
2 
8 
2 
2 



+2 
2 
8 
2 

+2 



Arg. 



135 
136 
137 
138 
139 
140 
141 
142 
143 
144 

145 
146 
147 
148 
149 
150 
151 
152 
153 
154 

155 
156 
157 
158 
159 
160 
161 
162 
163 
164 

165 
166 
167 
168 
169 
170 
171 
172 
173 
174 

175 
176 
177 

178 
179 
180 



+ 5 
61 
117 
174 
230 
286 
342 
398 
453 
509 

+ 563 
617 
670 
723 
774 
825 
875 
923 
971 
1017 

+1061 
1105 
1147 
1187 
1225 
1262 
1297 
1330 
1362 
1391 

+1419 
1445 
1468 
1489 
1509 
1526 
1541 
1554 
1564 
1573 

+1579 
1582 
1584 
1583 
1580 

+1575 



Diff. 



Vi 



+66 
56 
57 
66 
66 
66 
56 
55 
66 

64 

+54 
68 
58 

61 
61 
60 
48 
48 
46 



+44 
42 
40 
88 
87 
85 
88 
82 
20 

28 

+26 
28 
21 
20 
17 
15 
18 
10 
9 



+ 8 
+ 2 

- 1 
8 

- 5 



-1420 
1424 
1425 
1424 
1421 
1416 
1408 
1399 
1387 
1374 

-1358 
1340 
1320 
1298 
1274 
1248 
1221 
1191 
1159 
1126 

-1091 
1054 
1016 
976 
934 
891 
847 
801 
755 
707 

-657 
607 
556 
504 
452 
398 
344 
290 
235 
179 

- 124 

68 

- 12 
+ 44 

100 
+ 156 



Diff. 



- 4 

- 1 
+ 1 

8 
5 
8 
9 
12 
18 

16 

+18 
20 
22 
24 
26 
27 
80 
82 
88 

86 

+87 
88 
40 
42 
48 
44 
46 
46 
48 

60 

+60 
51 
52 
52 
54 
54 
64 
65 
66 

55 

+56 
66 
66 
60 

+66 



+ 76 
77 
79 
81 
83 
85 
86 
88 
89 
91' 

+ 92 
93 
94 
96 
97 
96 
99 
99 
100 
101 

+101 
102 
102 
102 
102 
103 
103 
102 
102 
102 

+102 

101 

101 

100 

99 

99 

98 

97 

96 

95 

+ 93 
92 
91 
90 

88 
+ 87 



Diff. 



+1 

2 
2 
2 
2 
1 
2 
1 
2 

1 

+1 
1 
2 
1 
1 
1 

1 
1 



+1 




+1 



-1 






-1 



1 
1 



1 
1 
1 
1 



-1 
1 
1 

2 
-1 



50 



TABLE lY .^Canlinued. 

PERTURBATIONS OF THE COORDINATES IN UNITS OF THE SIXTH DECIMAL. 

ARGUMENT H. 



Arg. 



180 
181 
182 
183 

184 
185 
186 

187 
188 
189 

190 
191 
192 
193 
194 
195 
196 
197 
198 
199 

200 
201 
202 

203 
204 
205 
206 
207 
208 
209 

210 
211 
212 
213 
214 
215 
216 
217 
218 
219 

220 
221 
222 
223 
224 
225 



+1575 
1567 
1557 
1545 
1531 
1514 
1496 
1475 
1452 
1427 

+1400 
1372 
1341 
1308 
1274 
1238 
1200 
1160 
1119 
1076 

+1032 
987 
941 
893 
844 
794 
743 
691 
639 
585 

+ 531 
477 
422 
367 
311 
256 
200 
144 
89 

+ 33 

^ 22 

77 

131 

185 

238 

- 291 



Diff. 


ni 




+ 156 


- 6 


811 


10 


266 


13 


321 


14 


375 


17 


428 


18 


481 


31 


533 


38 


584 


36 


635 


37 






+ 684 


-38 


732 


81 


779 


88 


825 


84 


670 


86 


913 


88 


955 


40 


995 


41 


1033 


43 


1071 


44 






+1106 


-45 


1140 


40 


1172 


48 


1202 


49 


1230 


50 


1256 


51 


1281 


53 


1303 


53 


1324 


54 


1342 


54 






+1358 


-54 


1373 


55 


1385 


55 


1395 


56 


1403 


55 


1409 


56 


1413 


56 


1414 


55 


1414 


56 


1412 



Diff. 



55 

-55 
54 

54 

58 

-58 



+1407 
1400 
1391 
1381 
1368 

+1353 



+55 
55 
55 

54 

53 
53 
53 
51 
51 

49 

+48 
47 
46 
45 
43 
43 
40 
38 
38 

85 

+84 
83 
80 
38 
36 
35 
33 
31 
18 

16 

+15 

13 

10 

8 

6 

4 

+ 1 



- 3 



- 7 

9 

10 

18 

-15 



+67 
85 
83 
82 
80 
78 
76 
74 
72 
70 

+68 
66 
64 
62 
60 
57 
55 
53 
51 
48 

+46 
44 
41 
39 
37 
34 
32 
30 
28 
25 

+23 

21 

19 

17 

15 

12 

10 

8 

6 

4 

+ 3 

+ 1 

^ 1 

3 

5 

-6 



Diff. 



-3 
3 
1 
3 
3 
3 
3 
3 
3 



-3 
3 
3 
3 
3 
3 
3 
3 
8 



-3 
8 
3 
3 
3 
3 
3 
3 
8 

3 

-3 
3 
3 
3 
8 
3 
3 
3 
3 



-3 
3 
3 
3 

-1 



Arg. 



225 
226 
227 
228 
229 
230 
231 
232' 
233 
234 

235 
236 
237 
238 
239 
240 
241 
242 
243 
244 

245 
246 
247 
248 
249 
%0 
251 
252 
253 
254 

255 
256 
257 
258 
259 
260 
261 
262 
263 
264 

265 
266 
267 
268 
269 
270 



- 291 
342 
393 
443 
492 
539 
586 
631 
675 
717 

. 758 

798 

836 

872 

907 

940 

971 

1001 

1028 

1054 

-1078 
1100 
1120 
1138 
1154 
1168 
1181 
1191 
1199 
1205 

-1210 
1212 
1213 
1211 
1208 
1203 
1196 
1187 
1177 
1165 

-1151 
1136 
1119 
1101 

1081 
-1060 



Diff. 



-51 
51 
50 
49 
47 
47 
45 
44 
43 

41 

-40 
38 
36 
35 
38 
31 
80 
37 
36 

• 34 

—33 

• 30 
18 
16 
14 
18 
10 

8 
6 



- 3 

- 1 
+ 3 

8 
5 
7 
9 
10 
13 

14 

+15 
17 
18 
30 

+31 



ni 



Diff. 



+1353 
1337 
1318 
1296 
1276 
1252 
1226 
1199 
1170 
1140 

+1108 

1075 

1040 

1004 

967 

929 

890 

850 

809 

767 

+ 7!d4 
681 
637 
593 
548 
503 
458 
412 
367 
321 

+ 276 

230 

185 

141 

96 

52 

+ 9 

- 34 
76 

118 

-^ 158 
198 
237 
274 
311 

- 347 



-16 
19 
SO 
33 
34 
36 
37 
39 
80 

33 

-38 
35 
36 
87 
38 
89 
40 
41 
43 

43 

-48 
44 
44 

45 
45 
45 
46 
45 
46 

45 

-46 
45 
44 
45 

44 
43 
48 
43 
43 

40 

-40 
39 
37 
87 

-86 



-6 
6 
10 
11 
12 
14 
15 
17 
18 
19 

-20 
21 
22 
23 
24 
25 
26 
27 
27 
28 

-29 
29 
30 
30 
31 
31 
32 
32 
32 
33 

-33 
33 
33 
33 
34 
34 
34 
34 
34 
34 

-34 
34 
34 
34 
34 

-34 



Diff. 



-3 
3 











-0 




-0 



51 



TABLE lY. —Cbniinued. 
PERTURBATIONS OP THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. 

ARGX7MSNT n. 



Arg. 



970 
271 
272 
273 
274 
275 
276 
277 
278 
279 

280 
281 
282 
283 
284 
235 
286 
287 
238 
289 

290 
291 
292 
293 
294 
295 
296 
297 
298 
299 

300 
301 
302 
303 
304 
305 
306 
307 
308 
309 

310 
311 
312 
313 
314 
315 



-1060 
1037 
1013 
988 
962 
935 
907 
878 
848 
618 

- 786 
754 
722 
689 
655 
621 
687 
552 
517 
483 

- 448 
413 
378 
344 
309 
275 
241 
208 
175 
143 

- Ill 

79 
48 

- 18 
+ 12 

41 

69 

96 

123 

148 

+ 173 
197 
221 
243 
265 

+ 2a5 



Diff, 



+M 
34 
36 
38 
37 
38 
39 
80 
80 

83 

+33 
83 
88 
S4 
84 
84 
85 
85 
84 

85 

+85 
85 

a4 

85 
84 
84 
88 

38 
83 

83 

+83 
81 
80 
80 
30 
38 
37 
37 
35 

35 

+34 
34 
33 
33 

+30 



Vl 



-347 
382 
415 
447 

478 
508 
536 
564 
590 
614 

-637 
658 
678 
607 
714 
730 
744 
757 
769 
779 

-788 
795 
801 
806 
810 
812 
813 
813 
811 
809 

•-805 
800 
795 
788 
780 
772 
762 
752 
741 
729 

-^717 
704 
690 
676 
662 

-647 



Diif. 



-85 
88 
33 
81 
30 
38 
38 
80 
34 

33 

30 
19 
17 
16 
14 
18 
13 
10 



- 7 
6 


4 
3 

- 1 


+ 3 
3 



+ 5 

5 

7 

8 

6 

10 

10 

11 

13 

13 

+18 
14 
14 
14 

+15 



-34 

34 
34 
34 
34 
34 
34 
34 
34 
34 

-34 
34 
84 
34 
34 

35 
35 
35 
35 

-36 
36 
86 
36 
37 
37 
37 
38 
38 
38 

-39 
39 
40 
40 
40 
41 
41 
42 
42 
43 

-43 
44 

44 
45 
45 



Diff. 



-0 












-0 






Axg* 



o 

315 
316 
317 
318 
J319 
320 
321 
322 
323 
324 

325 
326 
827 
328 
329 
330 
331 
332 
333 
334 

335 
336 
337 
338 
339 
340 
341 
342 
343 
344 

345 
346 
347 
348 
349 
350 
351 
352 
353 
354 

355 
356 
357 
358 
359 
360 



+365 
305 
324 
342 
359 
375 
391 
405 
419 
432 

+444 
455 
466 
476 
485 
493 
601 
508 
514 
520 

+525 
530 
534 
538 
541 
544 
547 
549 
551 
552 

+553 
554 
555 
556 
556 
556 
556 
556 
556 

^555 

+555 
554 
553 
553 
552 

+551 



Dtff. 



+30 
19 
18 
17 
16 
16 
14 
14 
18 

13 

+11 
11 
10 
9 
8 
8 
7 
6 
6 



+ 6 
4 
4 
8 
8 
8 
3 
3 
1 



+ 1 
1 

+ 1 






- 1 



- 1 
1 


1 
- 1 



Vi 



-647 
631 
615 
599 
583 
566 
549 
532 
575 
498 

-481 
463 
446 
429 
412 
394 
377 
360 
343 
327 

-310 
294 
277 
261 
245 
230 
214 
199 
184 
169 

-154 

140 

125 

111 

97 

83 

69 

56 

42 

29 

- 15 

- 2 
+ 11 

25 

38 

+ 51 



Diff. 



+16 
16 
16 
16 
17 
17 
17 
17 
17 

17 

+18 
17 
17 
17 
18 
17 
17 
17 
16 

17 

+16 
17 
16 
16 
15 
16 
15 
15 
15 

15 

+14 
15 
14 
14 
14 
14 
18 
14 
18 

14 

+18 
18 
14 
18 

+13 



(l 



-46 
46 
46 
47 

47 
48 
48 
48 
49 
49 

-49 
49 
50 
50 
50 
50 
50 
50 
50 
50 

-60 
50 
50 
50 
50 
49 
49 
49 
49 
48 

^8 
47 
47 
46 
46 
45 
45 
44 
43 
43 

-42 

41 
40 
40 
39 

-38 



Diff. 



-0 



1 



1 




1 





-0 

-1 
















+1 





1 



+1 



1 



1 



1 
1 



1 

c 

+1 

1 



1 

+1 



52 



TABLE lY .—Ctmiimed. 


PERTURBATIONS OF THE COORDINATES IN UNITS OF THE SIXTH DECIMAL. 


ARGUMENT III. 


Aig. 


6 


Diff. 


^1 


Diff. 


ll 


Diff. 


Arg. 


6 


Diff. 


<?1 


Diff. 


ll 


Diff. 


o 



+977 


-196 




+15 




o 
45 


+537 




-829 




- 7 




1 


973 


- 4 


213 


-17 






46 


522 


-15 


838 


-9 






2 


969 


4 


230 


17 


^ 


-3 


47 


506 


16 


847 


9 




-3 


3 


965 


4 


247 


17 


13 




48 


491 


15 


856 


9 • 


9 




4 


960 


5 


264 


17 




• 


49 


475 


16 


865 


9 






5 


955 


5 


281 


17 




1 


50 


460 


15 


873 


8 




1 


6 


950 


5 


298 


17 


12 




51 


444 


16 


881 


8 


10 




7 


945 


6 


314 


16 






52 


428 


16 


889 


8 






8 


939 


6 


331 


17 




1 


53 


412 


16 


896 


7 




3 


9 


933 


6 
6 


347 


16 
17 


11 




54 


395 


17 
16 


903 


7 
7 


12 




10 


+927 




«-364 








55 


+379 




-910 








11 


920 


- 7 


380 


-16 




3 


56 


363 


-16 


917 


-7 


• 


1 


12 


913 


7 


396 


16 


9 




57 


346 


17 


923 


6 


13 




13 


906 


7 


412 


16 






58 


329 


17 


929 


6 






14 


896 


8 


428 


16 




1 


59 


312 


17 


935 


6 




1 


15 


890 


8 


444 


16 


8 




60 


296 


16 


941 


6 


14 




16 


882 


8 


459 


15 






61 


279 


17 


946 


5 






17 


874 


8 


475 


16 




3 


62 


261 


18 


951 


5 




3 


18 


865 


9 


490 


15 


6 




63 


244 


17 


955 


4 


16 




19 


856. 


9 
9 


505 


16 
15 




1 


64 


227 


17 
17 


960 


5 
4 • 




1 


20 


+847 




-520 








65 


+210 




-964 








21 


838 


- 9 


535 


-15 


6 




66 


192 


-18 


967 


-8 


17 




22 


828 


10 


550 


15 




A 


67 


175 


17 


971 


4 






23 


818 


10 


564 


14 




3 


68 


158 


17 


974 


8 




1 


24 


808 


10 


578 


14 


3 




69 


140 


18 


977 


8 


18 




25 


797 


11 


592 


14 






70 


123 


17 


979 


3 






26 


786 


11 


606 


14 




1 


71 


105 


18 


981 


3 




1 


27 


775 


11 


620 


14 


+ 2 




72 


87 


18 


983 


3 


19 




28 


764 


11 


633 


13 






73 


70 


17 


985 


3 






29 


752 


12 


647 


14 
18 




3 


74 


52 


18 
17 


986 


1 
1 




1 


30 


+740 




-660 









75 


+ 35 




-987 




20 




31 


728 


-w 


673 


-13 






76 


+ 17 


-18 


988 


-1 






32 


716 


13 


685 


13 




1 


77 


- 1 


18 


989 


-1 




1 


33 


703 


13 


698 


18 


- 1 




78 


18 


•17 


989 





21 




34 


691 


11 


710 


13 






79 


36 


18 


989 









35 


678 


13 


722 


13 




3 


80 


53 


17 


988 


+1 




1 


36 


665 


18 


734 


13 


3 




81 


71 


18 


987 


1 


22 




37 


651 


14 


745 


11 






82 


88 


17 


986 


1 






38 


638 


13 


756 


11 




1 


83 


106 


18 


985 


1 




1 


39 


624 


11 

14 


768 


13 
11 


A 




84 


123 


17 
18 


983 


3 
3 


23 




40 


+610 




-779 








85 


-141 




-981 




. 




41 


595 


-15 


789 


-10 




3 


86 


158 


-17 


979 


+3 




1 


42 


581 


14 


800 


11 


6 




87 


175 


17 


977. 


3 


24 




43 


567 


14 


810 


10 






88 


192 


17 


974 


8 






44 


552 


15 


820 


10 




-1 


89 


209 


17 


971 


8 




-1 


45 


+537 


-15 


-829 


- 9 


- 7 




90 


-226 


-17 


-967 


+4 


-25 





53 



TABLE lY .—Cantimed. 

PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. 

ARGUICBNT m. 



Aig. 



Diff. 



n\ 



Diff. 



Diff. 



Aig. 



Diff. 



ni 



Diff. 



Diff. 



90 
91 
92 
93 
94 
95 
96 
97 
98 
99 

100 
101 
102 
103 
104 
105 
106 
107 
108 
109 

110 
111 
112 
113 
114 
115 
116 
117 
118 
119 

120 
121 
122 
123 
124 
125 
126 
127 
128 
129 

130 
131 
132 
133 
134 
135 



-226 
243 
260 
277 
294 
310 
327 
343 
359 
375 

-391 
407 
423 
438 
454 
469 
484 
499 
513 
528 

-543 
557 
571 
584 
598 
611 
625 
638 
651 
663 

-676 
688 
700 
711 
723 
734 
745 
756 
767 
777 

-787 
797 
806 
816 
825 

-834 



-17 
17 
17 
17 
16 
17 
16 
16 
16 

16 

-16 
16 
15 
16 
16 
16 
15 
14 
15 

14 

-15 
14 
18 
14 
13 
14 
13 
13 
19 

18 

-13 
13 
11 
13 
11 
11 
11 
11 
10 

10 

-10 



10 



- 



-967 
964 
960 
956 
951 
946 
941 
936 
930 
924 

-918 
911 
905 

898 
890 
883 
875 
767 
859 
850 

-«41 
832 
823 
813 
803 
793 
783 
772 
762 
751 

-740 
728 
717 
705 
693 
681 
668 
655 
643 
630 

-616 
603 
590 
576 
562 

-548 



+ 8 
4 
4 
6 
5 
5 
5 
6 
6 

6 

+ 7 
6 
7 
8 
7 
8 
8 
8 
9 

9 

+ 

10 
10 
10 
10 
11 
10 

11 
11 

+13 
11 
13 
13 
13 
18 
18 
13 
18 

14 

+13 
13 
14 
14 

+ 14 



-25 



26 



26 



27 



-I 



27 



28 



28 



28 



28 



28 



28 



28 



28 



28 



-1 











28 



-27 







+1 



135 
136 
137 
138 
139 
140 
141 
142 
143 
144 

145 
146 
147 
148 
149 
150 
151 
152 
153 
154 

155 
156 
157 
158 
159 
160 
161 
162 
163 
164 

165 
166 
167 
168 
169 
170 
171 
172 
173 
174 

175 
176 
177 

178 
179 
180 



-^34 

842 
850 
858 
866 
874 
881 
888 
894 
901 

-907 
913 
918 
924 
929 
933 
938 
942 
946 
950. 

-953 
956 
959 
961 
963 
965 
967 
968 
969 
970 

-970 
970 
970 
970 
969 
968 
967 
965 
964 
962 

-959 
957 
954 
950 
947 

-943 



-8 
8 
6 
8 
6 
7 
7 
6 
7 



-6 
5 
6 
5 

4 
5 

4 
4 
4 



-8 
8 
3 
3 
3 
S 
1 
1 

-1 






+1 
1 
1 
3 
1 
3 



+3 
8 

4 

8 

+4 



-548 
534 
519 
505 
490 
475 
460 
445 
430 
415 

-399 
384 
368 
352 
336 
320 
304 
288 
272 
255 

-239 
222 

206 
189 
172 
155 
139 
122 
105 
88 

-71 

54 
37 
20 
- 3 
+ 14 
31 
48 
65 
82 

+ 99 
116 
133 
150 
166 

+183 



+14 
16 
14 
15 
1ft 
16 
15 
16 
15 

16 

+15 
16 
16 
16 
16 
16 
16 
16 
17 

16 

+17 
16 
17 
17 
17 
16 
17 
17 
17 

17 

+17 
17 
17 
17 
17 
17 
•17 
17 
17 

17 

+17 
17 
17 
16 

+17 



-27 



27 



26 



26 



+0 



25 



25 



24 



23 



22 



21 



20 



19 



18 



17 



15 



-14 



+1 



54 



TABLE IV. Caniimied. 






PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SD:TH DECIMAL. 


AKGUMENT HI. 




1 


Arg. 


li 


Diff. 


Vl 


Diff. 


CI 


Diff. 


Arg. 


k 


Diff 


ni 


Diff. 


ii 


Diff. 


o 
180 

181 

182 


-943 

■ 939 

935 


+ 4 


+183 
200 
217 


+17 
17 


-14 


+1 


o 
225 

226 
227 


^24 
510 
496 


+ 14 
14 


+816 
826 
835 


+10 


+ 7 


+1 


183 


930 




233 


16 


13 




228 


482 


14 


844 




8 




184 


925 




250 


17 






229 


467 


15 


853 








185 


920 




266 


16 




1 


230 


453 


14 


862 






9 


186 


915 




283 


17 


12 




231 


438 


15 


871 




10 




187 


909 




299 


16 






232 


423 


15 


879 


O 






188 


903 


A 


315 


16 




9 


233 


409 


14 


887 






1 


189 


897 




331 


16 
16 


10 




234 


394 


15 
16 


895 




11 




190 
191 


-891 

884 


+ 7 


+347 
363 


+16 




1 


235 
236 


-378 
363 


+15 


+902 
909 


+ 7 


» 


1 


192 
193 


877 
870 




379 
395 


16 
16 


9 




237 

238 


348 
332 


15 
16 


916 
923 


mm 


12 




194 


863 




411 


16 




1 


239 


317 


15 


929 






9 


195 


855 


8 


426 


15 


8 




240 


301 


16 


935 




14 




196 
197 


847 
839 


8 
8 


442 
457 


16 
15 




3 


241 
242 


285 
269 


16 
16 


941 

947 






1 


198 


831 


8 


472 


16 


6 




243 


253 


16 


952 




15 




199 


822 


9 
9 


487 


15 
15 




1 


244 


237 


16 
16 


957 






1 


200 
201 


-813 

804 


+ 9 


+502 
517 


+15 


5 




245 
246 


-221 

205 


+16 


+961 
966 


+ 5 


16 




202 
203 


795 

785 


9 
10 


531 
546 


14 
15 




3 


247 

248 


189 
173 


16 
16 


970 
974 






1 


204 


776 


9 


560 


14 


3 




249 


156 


17 


977 




17 


- 


205 
2D6 


766 
755 


10 
11 


574 

588 


14 
14 




1 


250 
251 


140 
123 


16 
17 


980 
983 






S 


207 


745 


10 


602 


14 


- 2 




252 


107 


. 16 


986 




19 




208 
209 


734 
724 


11 
10 

11 


615 
629 


13 
14 

13 




3 


253 
254 


90 
74 


17 
16 

17 


988 
990 


3 
S 

9 




1 


210 
211 
212 


-713 
701 
600 


+ia 
11 


+642 
655 
668 


+18 
18 





1 


255 
256 
257 


- 57 
40 
24 


+17 
16 


+992 
993 
994 


+ I 

1 


20 


1 


213 
214 
215 
216 


678 
666 
654 
642 


19 
13 
13 
13 


681 
693 
705 
717 


18 
13 
13 
13 


+ 1 
3 


3 


258 
259 
260 
261 


- 7 

+ 10 

26 

43 


17 
17 
16 
17 


995 
995 
995 
995 


1 





21 
22 


1 


217 
218 


630 
617 


13 
18 


729 
741 


13 
13 




1 


262 
263 


60 

77 


17 

17 


995 
994 




- I 




1 


219 


604 


13 
18 


752 


11 
11 


4 

• 




264 


93 


16 

17 


993 


1 

9 


23 




220 
221 


-691 

578 


+18 


+763 
774 


+11 




1 


265 

266 


+110 
127 


+17 


+991 
990 


- 1 




1 


222 


565 


IS 


785 


11 


5 




267 


143 


16 


988 


9 


24 




223 
224 
2^ 


551 

538 

-524 


14 
18 

+14 


796 

806 

+816 


11 

10 

+10 


+ 7 


+3 


268 
269 
270 


160 

177 

+193 


17 
17 

+16 


985 
983 

+980 


8 

9 

- 8 


+24 


+0 



55 



TABLE lY .—C(yniimed. 






PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SDLTH DECIMAL. | 


AKGUMENT HI. 




1 


Arg. 


& 


Diff. 


ni 


Diff. 


& 


Diff. 


Arg. 


& 


Diff. 


^ 


Diff. 


Ci 


Diff 


o 
270 

271 

272 


+193 
210 
226 


+17 
18 


+980 
977 
973 




+24 


+1 


o 
315 

316 

317 


+^1 
830 
840 


+ e 

10 


+561 
547 
533 


-14 
14 


+28 


-0 


273 


242 


18 


969 


4 


25 




318 


849 





518 


16 


28 




274 


259 


17 


965 








319 


858 





502 


16 






275 


275 


16 


961 


4 




1 


320 


867 





486 


16 




1 


276 


291 


10 


956 




26 




321 


875 


8 


471 


16 


27 




277 

278 


307 
324 


16 
17 


951 
946 









322 
323 


883 
891 


8 
8 


455 
439 


16 
16 







279 


340 


16 


940 




26 




324 


899 


6 


423 


16 
16 


27 




280 
281 


+355 
371 


+16 


+934 
928 


— 




1 


325 

326 


+906 
913 


+ 7 


+407 
391 


-16 




1 


282 


387 


16 


921 




27 




327 


920 




375 


18 


26 




283 

284 


403 
418 


16 
15 


915 
908 









328 
329 


927 
933 




359 
342 


18 
17 




1 


285 


433 


16 


900 


' 


27 




330 


939 




325 


17 


25 




286 


449 


18 


893 








331 


945 




309 


16 






287 


464 


16 


885 






1 


332 


950 




292 


17 




1 


288 


479 


16 


876 




28 




333 


955 




275 


17 


24 




289 


494 


16 
16 


868 









334 


960 




258 


17 
17 







290 
291 


+509 
523 


+14 


+859 
850 


— 9 


28 




335 
336 


+964 
969 


+ 6 


+241 
224 


-17 


24 




292 
293 


538 
552 


14 


841 
831 




« 





337 
338 


973 
976 




206 
189 


18 
17 




1 


294 


566 


14 


822 




28 




339 


979 




172 


17 


23 




295 
296 


580 

594 


14 
14 


812 
801 






+1 


340 
341 


982 
985 




154 
137 


18 
17 




1 


297 


608 


14 


791 




29 




342 


967 


3 


120 


17 


22 




298 
299 


621 
635 


13 
14 

18 


780 
769 









343 
344 


989 
991 


3 
3 

3 


102 

84 


18 
18 

17 




1 


300 
301 
302 


+648 
661 
673 


+18 
13 


+757 
746 
734 


13 


29 





345 
346 
347 


+993 
994 
995 


+ 1 

+ 1 


+ 67 
49 
32 


-18 
17 


21 


1 


303 


686 


13 


722 




29 




348 


995 





+ 14 


18 


20 




304 
305 


698 
711 


13 
18 


710 
697 









349 
350 


995 
995 






- 4 
21 


18 
17 




1 


306 

307 
308 


723 
734 

746 


13 
11 
13 


685 
672 
659 




29 


-1 


351 
352 
353 


995 
994 
993 




- 1 
1 


39 

56 
74 


18 
17 
18 


19 


3 


309 


757 




11 
11 


645 




28 




354 


992 


1 

3 


91 


17 
18 


17 




310 
311 


+768 
779 


+11 


+632 
618 


-14 







355 
356 


+990 
988 


- 3 


-109 
126 


-17 




1 


312 


790 


11 


604 




28 




357 


985 


8 


144 


18 


16 




313 
314 
315 


801 

811 

+821 


11 

10 
+10 


590 

576 

4^1 


14 
-16 


+28 





358 
359 
360 


983 

980 

+977 


3 
3 

- 8 


161 

178 

-196 


17 

17 
-18 


+15 


-1 



56 



TABLE lY .—Cbnimued. 

PERTURBATIONS OF THE CO-ORDINATES IN UNITS OP THE SIXTH DECIMAL. 

ABGUMENT IV. 



Arg. 



h 



Diff. 



Vi 



Diff. 



Diff. 



Arg. 



Diff. 



Vi 



Diff. 



Diff. 




1 
2 
3 
4 
5 
6 
7 
8 
9 

10 
11 
12 
13 
14 
15 
16 
17 
18 
19 

20 
21 
22 
23 
24 
25 
26 
27 
28 
29 

30 
31 
32 
33 
34 
35 
36 
37 
38 
39 

40 
41 
42 
43 
44 
45 



^775 
773 
772 
770 
768 
765 
763 
760 
757 
754 

-750 
747 
743 
739 
735 
730 
725 
720 
715 
710 

-704 
699 
693 
687 
680 
674 
667 
660 
653 
645 

-638 
630 
622 
614 
605 
597 
588 
579 
570 
561 

-552 
542 
532 
523 
513 

-602 



+ 2 
1 

3 
3 
8 
3 
S 
8 
8 

4 

+ 8 

4 
4 
4 
5 
6 

5 
5 

6 

+ 5 
6 
6 
7 
6 
7 
7 
7 
8 



+ 8 
8 
8 
9 
8 
9 
9 
9 
9 

9 

+10 

10 

9 

10 

+11 



+ 75 
90 
106 
121 
137 
152 
167 
182 
197 
213 

+228 
243 
257 
272 
287 
302 
316 
331 
345 
359 

+374 
388 
402 
416 
430 
443 
457 
470 
484 
497 

+510 
523 
536 
549 
562 
574 
587 
599 
611 
623 

+635 

646 

658 

669 

. 680 

+691 



+15 
10 
15 
16 
15 
15 
15 
15 
16 

15 

+15 
14 
15 
15 
15 
14 
15 
14 
14 

15 

+14 
14 
14 
14 
13 
14 
18 
14 
13 

13 

+18 
18 
13 
IS 
13 
13 
13 
13 
13 

13 

+11 
13 
U 
11 

+ 11 



+38 



36 



35 



34 



32 



30 



29 



27 



25 



23 



21 



18 



15 



12 



3 



8 



-8 



+ 6 



45 
46 
47 
48 
49 
50 
51 
52 
53 
54 

55 
56 
57 
58 
59 
60 
61 
62 
63 
64 

65 
66 
67 
68 
69 
70 
71 
72 
73 
74 

75 
76 

77 
78 
79 
80 
81 
82 
83 
84 

85 
86 
87 
88 
89 
90 



•-502 
492 
482 
471 
460 
450 
439 
427 
416 
405 

-393 
382 
370 
358 
346 
334 
322 
310 
298 
285 

-273 
260 
248 
235 
222 
209 
196 
183 
170 
157 

-144 

130 

117 

103 

90 

76 

63 

49 

35 

21 

- 8 

+ 6 

20 

34 

48 

+ 62 



+10 
10 

11 
11 

10 

11 

13 
U 
11 

13 

+11 
13 
13 
13 
13 
13 
13 
13 
18 

13 

+18 
13 
18 
18 
18 
18 
18 
18 
18 

18 

+14 
18 
14 
13 
14 
18 
14 
14 
14 

13 

+14 
14 
14 
14 

+14 



+691 
702 
713 
723 
734 
744 
754 
763 
773 
782 

+791 
800 
809 
817 
825 
833 
841 
848 
856 
863 

+869 
876 
882 
888 
894 
899 
904 
909 
914 
918 

+922 
926 
929 
932 
935 
937 
940 
942 
943 
944 

+945 
946 
946 
946 
946 

+945 



+11 
11 

10 

11 

10 
10 


10 





+ 
9 
8 
8 
8 
6 
7 
8 
7 

6 

+ 7 
6 
6 
6 
5 
5 
5 
5 
4 

4 

+ 4 
8 
8 
3 
3 
8 
3 
1 
1 

1 

+ 1 




- 1 



+ 6 



+ 2 



- 2 



-4 



10 



15 



20 



25 



30 



35 



41 



46 



52 



57 



63 



-68 



6 



-5 



57 



TABLE lY.—Gmiinued. 






PEETUBBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. | 


ARGUMENT IV. 

t 




1 


Arg. 


6 


Diff. 


Vl 


Diff. 


ii 


Diff. 


Arg. 


& 


Diff. 


^1 


Diff. 


Ci 


Diff. 


o 
90 

91 

92 


+ 62 
77 
91 


+15 
14 


+945 
944 
943 


— 1 


-68 


-5 


o 

135 
136 
137 


4678 
690 
701 


+13 
11 


+605 
591 

578 


-14 
13 


-114 





93 


105 


14 


941 




73 




138 


712 


11 


564 


14 


114 




94 


119 


14 


939 








139 


723 


11 


550 


14 




I _ 


95 


133 


14 


937 






5 


140 


734 


11 


536 


14 




+1 


96 


147 


14 


935 




78 




141 


745 


11 


522 


14 


113 




97 
98 


162 
176 


15 
14 


932 
929 






5 


142 
143 


755 
765 


10 
10 


507 
493 


15 
14 




I 


99 


190 


14 
14 


925 




83 




144 


775 


10 


478 


15 
15 


112 




100 
101 


+204 
219 


+15 


+921 
917 


— 4 




4 


145 
146 


+784 
794 


+10 


+463 

448 


-15 




3 


102 


233 


14 


912 




87 




147 


803 




433 


15 


110 




103 
104 


247 
262 


14 
15 


908 
903 






5 


148 
149 


812 
820 




418 
403 


15 

15 




3 


105 


276 


14 


897 




92 




150 


828 




388 


15 


108 




106 


290 


14 


891 








151 


836 




372 


16 






107 


305 


15 


885 






4 


152 


844 




357 


15 




3 


108 
109 


319 
333 


14 
14 

14 


879 
872 




96 


8 


153 
154 


851 

858 




341 
325 


16 
16 

16 


105 


3 


110 
111 


+347 
362 


+15 


+865 
858 


— 7 


99 




155 
156 


+865 
872 


+ 7 


+309 
293 


-16 


102 




112 
113 


376 
390 


14 
14 


851 
843 






4 


157 

158 


878 
884 




277 
261 


16 
16 




8 


114 


404 


14 


835 




103 




159 


889 




245 


16 


99 




115 
116 


418 
432 


14 
14 


826 
817 






3 


160 
161 


894 
899 




229 

213 


16 
16 




4 


117 
118 
119 


446 
459 
473 


14 
13 
14 

14 


808 
799 
790 




106 


3 


162 
163 
164 


904 
908 
912 




197 
181 
164 


16 
16 
17 

16 


95 


4 


120 
121 
122 


+487 
500 
514 


+13 
14 


+780 
770 
760 


— JQ 


108 


3 


165 
166 
167 


+915 
918 
921 


+ 8 


+148 
132 
115 


-16 
17 


91 


5 


123 


527 


13 


749 




110 




168 


923 




99 


16 


86 




124 
125 


541 
554 


14 
18 


738 
727 






3 


169 
170 


925 
927 




83 
67 


16 
16 




5 


126 


567 


13 


716 




112 




171 


928 


ff . 


50 


17 


81 




127 
128 


580 
593 


13 
IS 


704 
693 






1 


172. 
173 


929 
929 


+ 1 



34 
18 


16 
16 




6 


129 


605 


13 
13 


681 




113 




174 


929 






+ 1 


17 
16 


76 




130 
131 


+618 
630 


+15 


4€69 
656 


—13 




-1 


175 
176 


+929 
928 


- 1 


- 15 
31 


-16 




6 


132 


643 


13 


644 




114 




177 


927 


1 


47 


16 


70 




133 
134 
135 


655 
667 

+678 


12 

13 

+11 


631 

618 

+605 


—13 


-114 





178 
179 
180 


926 
924 

+922 


1 

3 

- 3 


63 

79 
- 95 


16 

16 

-16 


-64 


+6 



8 



58 



TABLE lY.—OniAmecL 

PEETURBATI0N8 OP THE CO-OEDINATES IN UNITS OF THE SIXTH DECIMAL. 

ARGUMENT IV. 



Afg. 



180 
181 
182 
163 
184 
185 
186 
187 
188 
189 

190 
191 
192 
193 
194 
195 
196 
197 
198 
199 

200 
201 
202 
203 
204 
205 
206 
207 
208 
209 

210 
211 
212 
213 
214 
215 
216 
217 
218 
219 

220 
221 
222 
223 
224 
225 



+922 
919 
916 
913 
909 
905 
901 
896 
691 
885 

+879 

873 
sum 

859 
852 
844 
836 
828 
819 
810 



Diff. 



- 8 
8 
8 

4 
4 
4 
5 
6 
6 

6 

- 6 
7 
7 
7 
8 
8 
8 
9 
9 



ni 





9 


+801 




791 


-10 


761 


10 


771 


10 


760 


11 


749 


11 


738 


11 


727 


11 


715 


19 


703 


13 




13 


+691 




678 


-18 


665 


13 


652 


18 


639 


18 


626 


IS 


612 


14 


598 


14 


584 


14 


570 


14 




15 


+555 




541 


-14 


526 


Iff 


511 


15 


496 


15 


+481 


-Iff 



-95 
111 
127 
143 
158 
174 
190 
205 
^1 
236 

-asi 

266 
281 
^296 
311 
326 
340 
355 
369 
383 

-397 
411 
425 
438 
452 
466 
479 
492 
505 
518 

-530 
543 
555 
567 
579 
591 
603 
614 
626 
637 

-648 
658 
669 
679 
690 

-700 



Diff- 



-15 

16 
16 
15 
16 
16 
15 
16 
15 

15 

-15 
15 
15 
15 
15 
14 
15 
14 
14 

14 

-14 
14 
18 
14 
14 
18 
13 
18 
18 

13 

-18 
13 
13 
13 
13 
13 
11 
13 
11 

11 

-10 
11 
10 
11 

-10 



-^ 



58 



52 



45 



38 



31 



S4 



17 



10 



- 3 



+ 4 



11 



18 



25 



Diff. 



31 



+38 



+6 



6 



Arg. 



6 



+7 



225 
226 
227 
228 
229 
230 
231 
232 
233 
234 

235 
236 
237 
238 
239 
240 
241 
242 
243 
244 

245 

246 
247 
248 
249 
250 
251 
252 
253 
254 

255 
256 
257 
258 
259 
260 
261 
262 
263 
264 

265 

266 
267 
268 
269 
270 



+461 
465 
450 
434 
419 
403 
387 
371 
355 
339 

+323 
307 
291 
274 
258 
242 
226 
210 
193 
177 

+161 

145 

129 

113 

97 

81 

65 

49 

34 

18 

+ 3 

- 13 

28 

43 

58 

73 

88 

102 

117 

131 

-145 
160 
174 
187 
201 

-214 



Diff. 



-16 
15 
16 
15 
16 
16 
16 
16 
16 

16 

-16 
16 
17 
16 
16 
16 
16 
17 
16 

16 

-16 
16 
IC 
16 
16 
16 
16 
15 
16 

15 

-16 
16 
15 
15 
15 
15 
14 
15 
14 

14 

-15 
14 
18 
14 

-18 



ni 



-700 
710 

719 
729 
736 
747 
756 
764 
773 
781 

-789 
797 
805 
812 
819 
826 
833 
839 
846 
652 

-857 
863 
866 
873 
878 
883 
887 
891 
895 
899 

-902 
905 
908 
911 
913 
915 
917 
919 
920 
921 

-922 
922 
922 
922 
922 

-921 



DiC 



-10 
9 

9 
9 
9 
8 
9 
8 

8 

- 6 
8 
7 
7 
7 
7 
6 
7 
6 



- 6 
6 
5 
5 
5 
4 
4 
4 
4 



- 3 
8 
8 
3 
3 
3 
3 
1 
1 

- 1 





+ 1 



+38 



44 



50 



56 



61 



€6 



71 



75 



79 



82 



86 



88 



90 



92 



DiC 



93 



+94 



+6 



+1 



59 





TABLE lY.^amtimed. 


PEETDBBATIONS OP THE CO-OBDINATES IN CKITS OF THE SIXTH DECIMAIi, | 


• 


ARGUMENT IV. 


1 


Aig. 


«i 


Diff. 


Vi 


Diff. 


il 


Diff. 


Aig. 


«i 


Diff. 


Vi 


Diff. 


Cl 


Diff. 


o 
270 

271 

272 


-214 
228 

241 


-14 
13 


-921 
920 
919 


+ 1 

1 


+94 


+1 


o 
315 

316 

317 


-652 
658 
664 


6 


-600 
587 
574 


+13 
18 


+71 


-8 


273 


254 


18 


917 


3 


95 




318 


670 


6 


661 


18 


68 




274 
275 


267 
279 


13 
13 


915 
913 


3 
3 







319 
320 


676 
681 


6 


548 
635 


18 
13 




8 


276 


292 


IS 


911 


3 


95 




321 


687 




521 


14 


65 




277 

278 


304 
316 


13 
13 


908 
905 


8 
8 




-I 


322 
323 


692 
697 




507 
493 


14 
14 




8 


279 


328 


13 
13 


902 


8 

4 


94 




324 


702 




479 


14 

14 


62 




280 
281 


-340 
352 


-13 


-898 
894 


+ 4 







325 
326 


-707 
712 


—5 


-465 
450 


+lfi 




3 


282 


363 


11 


890 


4 


94 




327 


716 




436 


14 


60 




283 


375 


13 


886 


4 






328 


721 




421 


16 




A 


284 


386 


11 


881 


6 




1 


329 


725 




406 


15 




3 


285 


397 


11 


876 


A 


93 




330 


729 




392 


14 


57 




286 


408 


11 


871 


5 




m 


331 


733 




377 


15 

• 




g^ 


287 


418 


10 


865 


6 




I 


332 


737 




362 


IS 




3 


288 


429 


11 


859 


6 


92 




333 


741 




347 


15 


65 




289 


439 


10 
10 


853 


8 
tf 




3 


334 


744 




332 


16 
16 




8 


290 
291 


-449 
459 


-10 


-^7 

840 


+ 7 


90 




335 
336 


-748 
751 


-8 


-^16 
301 


+16 


52 




292 


469 


10 


833 


7 




A 


337 


754 




286 


16 




A 


293 


479 


10 


825 


8 




3 


338 


757 




270 


16 




3 


294 
295 


488 
497 


9 
9 


818 

8io 


7 

8 


88 


A 


339 
340 


760 
762 


3 


255 

239 


16 

16 


50 


A 


296 


507 


10 


802 


8 




3 


341 


765 


8 


223 


16 




3 


297 


516 


9 


793 


9 


86 




342 


767 


3 


208 


16 


48 




298 


524 


8 


785 


8 




A 


343 


769 


3 

4% 


192 


16 




A 


299 


533 


9 



776 








3 


344 


771 


3 

3 


177 


16 
16 




3 


300 
301 
302 


•-542 
550 
558 


- 8 
8 


-767 

757 
747 


+10 
10 


84 


3 


345 

. 346 

347 


-773 
774 
775 


-1 


-161 
145 
129 


+10 
16 


46 


3 


303 


566 


8 


737 


10 


81 




348 


776 




114 


16 


44 




304 


574 


8 


727 


10 




A 


349 


777 




98 


16 




« 


305 


562 


8 


717 


10 




3 


350 


778 




82 


16 




1 


306 


590 




706 


11 


79 




351 


779 




66 


16 

a mm 


43 




307 


597 




695 


11 




m 


352 


779 


—0 


51 


16 




A 


308 


604 




684 


11 




9 


353 


779 





35 


16 




3 


309 


612 




673 


11 
13 


76 




354 


779 






19 


16 

16 


41 




310 
311 


-619 
626 


— 7 


-661 
649 


+13 




3 


355 
356 


-779 
779 




_|_ - 


- 3 
+ 12 


+15 




3 


312 


632 




637 


13 


73 




357 


778 


+1 


28 


16 


39 




313 
314 
315 


639 

645 

-652 


— 7 


625 
613 

-600 


13 

13 

+13 


+71 


-3 


358 
359 
369 


777 

776 

-775 


1 

1 

+1 


44 

69 

+ 75 


16 
16 

+16 


+38 


-1 



60 



TABLE IV. Cbntinued. 






PERTURBATIONS OF THE COORDINATES IN UNITS OF THE SIXTH DECIMAL, j 


ARGUMENT V. 






Arg. 


h 


Diff. 


Vl 


Diff. 


ii 


Diff. 


Arg. 

o 
135 

138 


& 


Diff 


m 


Diff. 


ii 


Diff. 


o 


3 


-507 
507 




1 tf« 


+ 52 
39 


-IS 


- 84 
77 


+7 


+358 
376 


+18 


-188 
181 


+ 7 


+150 

148 


-3 


6 


505 


+ 3 


26 


13 


70 


7 


141 


392 


16 


174 


7 


146 


3 


9 


502 


3 


+ 13 


13 


63 


7 


144 


408 


16 


166 


8 


144 


3 


12 


497 


5 





13 


56 


7 


147 


422 


14 


158 


8 


141 


8 


15 


491 


6 


- 13 


18 


49 


7 


150 


436 


14 


150 


8 


137 


4 


18 


484 


7 


26 


IS 


41 


6 


153 


448 


13 


141 


9 


133 


4 


21 
24 


475 

465 


9 
10 


39 
52 


IS 
13 


33 
25 


8 
8 


156 
159 


459 
469 


11 
10 


132 
122 


9 
IC 


129 
125 


4 
4 


27 


454 


11 
13 


64 


13 
18 


18 


7 
8 


162 


477 


8 
7 


113 


9 
10 


120 


6 
6 


30 
33 


-441 
427 


+14 


- 77 
89 


-13 


- 10 

- 2 


+8 


165 
168 


+484 
490 


+ 6 


-103 
92 


+11 


+115 
109 


-6 


36 


412 


15 


100 


11 


+ 6 


8 


171 


494 


4 


82 


10 


103 


6 


39 
42 


396 
379 


16 
17 


112 
123 


13 
11 


14 
22 


6 
8 


174 
177 


497 
499 


3 

+ 3 


71 
61 


11 
10 


97 
91 


6 
6 


45 

48 


360 
340 


19 


133 
143 


10 
10 


30 
38 


8 
8 


180 
183 


499 
498 




- 1 


50 
39 


11 
11 


84 
78 


7 
6 


51 


320 


20 


153 


10 


45 


7 


186 


496 


3 


28 


11 


71 


7 


54 


299 


21 


163 


10 


53 


8 


189 


493 


8 


16 


12 


63 


8 


57 


277 


33 
38 


171 


8 
8 


60 


7 
8 


192 


488 


6 

6 


- 5 


11 
11 


56 


7 
8 


60 
63 


-254 
230 


+24 


-179 

187 


- 8 


+ 68 
75 


+7 


195 

198 


+482 
474 


- 8 


+ 6 
18 


+ 13 


+ 48 
41 


-7 


66 


206 


34 


194 


7 


82 


7 


201 


465 


9 


29 


11 


33 


8 


69 


181 


36 


201 


7 


88 


6 


204 


455 


10 


40 


11 


25 


8 


72 
75 


156 
130 


36 
36 


207 
212 


6 
6 


95 
101 


7 
6 


207 
210 


444 
432 


11 
13 


51 
63 


11 
12 


17 
9 


8 
8 


78 
81 


104 

78 


36 
36 


216 
220 


4 
4 


107 
112 


6 
6 


213 
216 


418 
404 


14 
14 


74 
84 


11 
10 


+ 1 
- 7 


8 
8 


84 


51 


37 


224 


4 


118 


6 


219 


388 


16 


95 


11 


15 


8 


87 


- 25 


36 
37 


226 


3 
3 


123 


6 

4 


222 


371 


17 

17 


106 


11 
10 


23 


8 
8 


90 
93 
96 


+ 2 
29 
55 


+27 
36 


-228 

230 
231 


- 3 


+127 
131 
135 


+4 
4 


225 

228 
231 


+354 
335 
316 


-19 
19 


+116 
126 
136 


+10 
10 


- 31 
39 
47 


-8 
8 


99 


81 


36 


231 


1 M 


139 


4 


234 


295 


31 


145 


9 


54 


7 


102 


107 


36 


230 


+ 1 


142 


8 


237 


274 


31 


154 


9 


61 


7 


105 


133 


36 


229 




145 


8 


240 


252 


33 


163 


9 


69 


8 


108 


159 


36 


228 




147 


3 


243 


230 


33 


172 


9 


76 


7 


111 


184 


36 


226 




149 


3 


246 


207 


38 


180 


8 


83 


7 


114 


208 


34 


223 




151 


3 


249 


183 


34 


187 


7 


89 


6 


117 


232 


34 
28 


219 




152 


1 
+ 1 


252 


158 


36 

36 


194 


7 

7 


C6 


7 
6 


120 
123 


+255 
277 


+23 


-215 
211 


+ 4 . 


+153 
153 





255 
258 


+133 

108 


-36 


+201 
207 


+ 6 


-102 
107 


-6 


126 
12f) 


298 
319 


31 
31 


206 
200 




153 
152 



-1 


261 
264 


83 
57 


36 
36 


213 
218 


6 
6 


113 
118 


6 
6 


132 
135 


339 

+358 


20 
+19 


194 

-188 


+ 1 ^^1 

® +150 


1 
-1 


267 

270 


31 

+ 5 


36 
-36 


222 

+226 


4 
+ 4 


123 
-127 


6 
-4 



61 



TABLE lY .—dnOinued. 

PERTURBATIONS OF THE COORDINATES IN UNITS OF THE SIXTH DECIMAL. 

AKGUMENT V. 



Arg. 

o 
270 

273 

276 

279 

!^2 

285 

288 

291 

294 

297 

300 
303 
306 
309 
312 
315 



«l 


Diff. 


ni 


Diff. 


Cl 


Diff. 


Arg. 

o 
315 

318 


h 


Diff. 


ni 


Diff. 


tl 


+ 5 
-21 


-96 


+226 
229 


+3 


-127 
132 


-5 


-351 
370 


-19 


+205 
199 


- 6 


-149 
147 


47 


96 


232 




135 


8 


321 


387 


17 


191 


8 


145 


72 


95 


234 




139 


4 


324 


404 


17 


183 


6 


142 


98 


96 


235 


t . 


142 


8 


•327 


420 


16 


175 


8 


139 


124 


96 


236 


+1 


145 


8 


330 


434 


14 


166 


9 


136 


149 
174 


9A 
96 


236 
235 


-1 


147 
149 


9 
9 


333 
336 


447 
459 


18 
19 


156 
146 


10 
10 


132 
128 


198 


94 


234 




150 


1 


339 


470 


11 


136 


10 


124 


222 


94 
98 


232 




151 


1 

-1 


342 


479 




8 


125 


11 
19 


119 


-245 
268 


-9» 


+229 
226 


—8 


-152 
152 





345 

348 


-487 
494 


- 7 


+113 
102 


-11 


-114 
109 


290 


99 


222 




152 





351 


499 


6 


90 


19 


103 


311 


91 


217 




151 


+1 


354 


503 


4 


77 


18 


97 


332 
-351 


91 
-19 


211 

+205 


-« 


150 
-149 


1 

+1 


357 
360 


506 
-507 


8 
- 1 


65 
+ 52 


19 
-18 


91 

- 84 



Diff. 



+9 
9 
8 
8 
8 



6 

+7 



ARGUMENT VI. 



Arg, 





3 

6 

9 

12 

15 

18 

21 

24 

27 

30 
33 
36 
39 
42 
45 
48 
51 
54 
57 

60 
63 
66 

69 



+492 
488 
483 
477 
470 
461 
451 
440 
428 
414 

+400 
384 
367 
349 
330 
311 
290 
269 
247 
224 

+201 
177 
152 

+127 



Diff. 


^1 


Diff. 


tl 




+ 54 







*"* A 


79 


+96 






104 


98 







129 


96 






153 


94 


-1 




177 


94 






200 


98 


1 




223 


98 






245 


99 


2 




267 


91 








91 






+288 




2 


***lo 


308 


t90 






327 


19 


2 




346 


19 






363 


17 


3 




379 


16 




91 


395 


16 


3 


91 


409 


14 




99 


423 


14 


3 


98 


435 


19 




98 




11 






+446 




4 


-94 


455 


+ 




96 


464 





_4 


-98 


+471 


+ 7 





Arg. 



69 
72 

75 
78 
81 
84 
87 
90 
93 
96 

99 
102 
105 
108 
111 
114 
117 
120 
123 
126 

129 
132 
135 
138 



+127 

102 

77 

51 

+ 25 

- 1 

27 

53 

78 

104 

-129 
154 
179 
203 
226 
249 
271 
293 
314 
333 

-352 
370 
387 

-403 



Diff. 


% 


Diff 




+471 




-96 


477 


+ 6 


96 


482 




96 


485 




96 


487 




96 


488 


+ 1 


96 


487 


^^ 1 


96 


485 




96 


482 




96 


477 




96 


+471 




-96 


464 


- 7 


96 


455 




94 


446 




98 


435 




98 


422 




99 


409 




99 


394 




91 


379 




10 


362 




19 


-344 


18 


-18 


326 


-18 


17 


306 


90 


-16 


-286 


-90 



& 



-4 

4 
4 
5 
5 



-3 



62 



TABLE lY .—(hntimed. 

PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. 

ARGUMENT VI. 



Arg. 



138 
141 
145 
147 
150 
153 
156 
159 
162 
165 

168 
171 
174 
177 
180 
183 
186 
189 
192 
195 

198 
201 
204 
207 
210 
213 
216 
219 
222 
225 

228 

231 
234 
237 
240 
243 
246 
249 



-403 
418 
431 
444 
455 
465 
474 
481 
487 
492 

-495 
497 
498 
497 
495 
491 
486 
480 
472 
464 

-454 
442 
430 
416 
401 
385 
368 
349 
330 
310 

-290 
268 
246 
223 
199 
175 
150 

-125 



Diff. 



-15 

13 

18 

11 

10 

9 

7 

6 

ff 



- 3 

- 1 

+ 1 
3 
4 
6 
tf 
8 
8 

10 

+13 
13 
14 
16 
18 
17 
19 
19 
30 

30 

+33 
33 
38 
34 
34 
36 

+36 



ni 



+286 
265 
243 
^0 
197 
173 
149 
124 
99 
74 

+ 48 

+ 23 

- 3 

29 

54 

80 

105 

130 

155 

179 

-202 
225 
248 
270 
291 
311 
330 
349 
366 
383 

-398 
412 
426 
438 
448 
458 
466 

-473 



Diff. 



-31 
33 
38 
38 
34 
34 
35 
35 
35 

38 

-35 
38 
38 
35 
38 
35 
35 
35 
34 

38 



38 
33 
31 
30 
10 
19 
17 
17 

15 

-14 
14 
13 
10 
10 
6 

• 7 



Cl 



-3 
3 
3 
2 
2 

1 

-1 





+1 

1 
2 
2 
2 
3 

3 
4 
4 

+4 



Arg. 



o 
249 

252 

255 
258 
261 
264 
267 
270 
273 
276 

279 
282 
285 

288 
291 
294 
297 
300 
303 
306 

309 
312 
315 
318 
321 
324 
327 
330 
333 
336 

339 
342 
345 
348 
351 
354 
357 
360 



-125 

100 

74 

48 

-22 

+ 4 

30 

56 

81 

107 

+132 
157 
161 
205 
228 
251 
273 
294 
314 
334 

+353 
370 
387 
402 
417 
430 
442 
453 
463 
472 

4479 
485 
489 
492 
494 
495 
494 

4492 



Diff. 



+35 
38 
38 
38 
38 
38 
38 
35 
38 

35 

+35 
34 
34 
38 
38 
33 
31 
30 
30 

19 

+17 
17 
15 
15 
18 
13 
11 
10 
9 



+ 8 
4 
8 
3 

+ 1 

- 1 

- 3 



ni 



-473 
479 
483 
486 

488 
488 
487 
485 
481 
476 

-470 
462 
453 
443 
432 
420 
406 
391 
376 
359 

-341 
323 
303 
283 
262 
240 
217 
194 
171 
147 

-132 
98 
73 
47 

- 22 

+ 3 
29 

+ 54 



Diff. 



- 8 

4 
8 

- 3 


+ 1 
3 
4 
5 



+ 8 
9 
10 
11 
13 
14 

'15 
15 
17 

18 

+18 
30 
30 
81 
33 
38 
38 
38 
34 

35 

+34 
35 
38 
35 
35 
38 

+35 



+4 
4 
5 
5 
5 

5 
5 
4 
4 
4 

4 
3 
3 
3 
2 

2 
1 

+1 








63 



TABLE I Y.— Continued. 








PERTURBATIONS OF THE CO-ORDINATES IN UNITS OP THE 


SIXTH 


: DECIMAL. 1 


ARGUMENT VH 








Arg. 


«i 


Diff. 


Vl 


Diff. 


& 


Arg. 


6 


Diff. 


m 


Diff. 


(l 





3 
6 
9 


-231 
232 
233 
234 


- 1 
1 

1 


- 4 

8 
13 

18 




-20 
21 


o 
135 

138 

141 

144 


+292 
322 
350 
377 


+80 

38 
37 


-400 
383 
364 
342 


+17 
19 
33 


+ 8 
10 


12 


236 


3 


23 




22 


147 


403 


36 


319 


88 




15 


238 


3 


29 






150 


426 


38 


293 


36 


13 


18 


240 


3 


35 




23 


153 


448 


33 


266 


37 




21 
24 


243 
245 


8 
3 


42 

50 


8 


24 


156 
159 


468 
485 


30 
17 


236 

205 


80 
81 


15 


27 


248 


8 
3 


58 


8 




162 


500 


18 


173 


83 
88 


16 


30 
33 
36 


-250 
253 
255 


- S 

3 


-67 

77 
88 


-10 
11 


24 
24 


165 
168 
171 


+513 
522 
529 


+ 9 
7 


-140 

^ 106 

70 


+84 
86 


18 


39 
42 
45 


256 
258 
258 


1 

- 3 




99 
112 
126 


11 

18 
14 


23 


174 
177 
180 


533 
534 
533 


4 
+ 1 
- 1 


- 35 

+ 1 

37 


86 
86 
86 


19 

20 


48 


258 





140 


14 


23 


183 


528 


6 


72 


88 




51 


258 




1 _ 


155 


16 




186 


521 


7 


107 


86 


21 


54 


256 


+ 3 


171 


10 


22 


189 


511 


10 


142 


86 




57 


253 


8 

4 


187 


16 
17 




192 


496 


18 
16 


175 


88 

83 


22 


60 
63 


-249 
244 


+ 5 


-204 
222 


-18 


21 


195 
198 


+482 
464 


-18 


+207 
238 


+81 


22 


66 


237 


7 


239 


17 


19 


201 


444 


30 


267 


39 




69 


229 


8 


257 


18 




. 204 


422 


33 


294 


37 


23 


72 


220 


9 


275 


18 


18 


207 


398 


34 


320 


36 




75 


209 


11 


293 


18 




210 


372 


36 


343 


38 


23 


78 


196 


IS 


311 


18 


16 


213 


345 


37 


364 


31 




81 


182 


14 


328 


17 




216 


316 


39 


383 


19 


22 


84 


166 


16 


345 


17 


14 


219 


266 


80 


400 


17 




87 


149 


17 
30 


362 


17 
16 




222 


256 


80 
81 


414 


14 
11 


22 


90 
93 


-129 
109 


+30 


-377 
391 


-14 


12 


225 

228 


+225 
194 


-81 


+425 
434 


+ 9 


21 


96 


86 


38 


404 


18 


9 


231 


162 


83 


441 


7 




99 


62 


34 


416 


13 




234 


131 


81 


445 


4 

1 _, 


20 


102 


37 


35 


426 


10 


7 


237 


100 


81 


447 


+ 3 




105 

108 


- 10 
+ 18 


37 
38 


434 
441 


6 
7 


4 


240 
243 


69 
40 


81 
39 


447 
444 



- 8 


19 


111 


47 


39 


445 


4 




246 


+ 11 


39 


440 


4 


18 


114 


76 


39 


448 


- 8 


-2 


249 


- 17 


38 


433 


7 




117 


107 


81 
81 


448 



+ 3 




252 


44 


37 
36 


424 


9 
10 


17 


120 
123 


+138 
169 


+81 


-446 
442 


+ 4 


+ 1 


255 

258 


-69 
93 


-34 


+414 
402 


-13 


• 

15 


126 


200 


81 


435 


7 


3 


261 


115 


33 


389 


IS 




129 


231 


81 


426 


9 




264 


136 


31 


375 


14 


13 


132 
135 


262 

+292 


81 

+80 


414 
-400 


13 

+14 


+ 6 


267 

270 


155 
-172 


19 
-17 


360 
+344 


16 
-16 


+11 



64 



TABLE lY.— Caniinued. 

PERTURBATIONS OF THE CO-ORDINATES IN UNITS OP THE SIXTH DECIMAL. 

ARGUMENT VIL 



Arg. 



270 
273 
276 
279 
282 
285 
288 
291 
294 
297 



-172 
188 
202 
214 
225 
234 
242 
248 
253 
257 



300 


-260 


303 


261 


306 


262 


309 


262 


312 


261 


315 


-259 



Diff. 


Vl 


Diff. 


fl 




+344 




+11 


-16 


327 


-17 




14 


309 


18 


9 


13 


202 


n 




11 


274 


18 


7 




256 


18 






238 


18 


5 


• " 


220 


16 






203 


17 


+ 3 




186 


17 




^ 




16 






+170 







^"^ 1 


155 


-16 




^^ \ 


140 


16 


- 2 




126 


14 




+ 1 


112 


14 


- 4 


+ 3 


+100 


-13 





Arg. 



o 
315 

318 

321 

324 

327 

330 

333 

336 

339 

342 

345 
348 
351 
354 
357 
360 



-259 
257 
255 
252 
249 
247 
244 
241 
239 
237 

-235 

233 
232 
231 
231 
-231 



Diff. 


Vi 


Diff. 




+100 




+3 


88 


-13 


3 


78 


10 


S 


68 


10 


8 


59 




3 


51 




8 


43 




3 


36 




3 


30 




3 


24 




3 


+ 19 




+3 


14 


^" A 


1 


9 




+1 


5 







+ 1 







- 4 





ii 



- 7 

9 

11 

13 

15 

17 

19 
-20 



ARGUMENT VUL 



Afg. 




3 
6 
9 

12 
15 
18 
21 
24 
27 

30 
33 
36 
39 
42 
45 
48 
51 
54 
57 

60 
63 
66 
69 



-352 
350 
347 
344 
339 
334 
328 
320 
312 
303 

-294 
283 
272 
260 
247 
233 
219 
204 
189 
173 

-157 
140 
123 

-106 



Diff. 



+ 3 

8 
3 

6 
6 
6 
8 
8 
9 

9 

+11 
11 
13 
13 
14 
14 
16 
16 
16 

16 

+17 
17 

+17 



Vl 



Diff. 



+ 22 

40 

58 

76 

94 

112 

129 

146 

163 

179 

+194 
209 
224 
238 
251 
263 
275 
286 
296 
306 

+314 
322 
329 

+335 



+18 
18 
18 
16 
18 
17 
17 
17 
16 

16 

+15 
16 
14 
13 
13 
13 
11 
10 
10 

8 

+ 8 

7 

+ 6 



-7 

6 
5 
4 
3 

2 

-1 



+2 

3 

4 

+5 



Ai^. 



69 
72 
75 

78 
81 
64 
87 
90 
93 
96 

99 
102 
105 
108 
111 
114 
117 
120 
123 
126 

129 
132 
135 
138 



6 


Diff. 


fll 


Diff. 


-106 




+335 




88 


+18 


340 


+ 6 


70 


16 


344 


4 


52 


18 


347 


3 


34 


16 


349 


3 


- 15 


19 


350 


1 


+ 3 


18 


351 


+ 1 


22 


19 


350 


- 1 


40 


18 


348 


3 


58 


18 


346 


3 




18 




4 


+ 76 




+342 




94 


+18 


338 


- 4 


112 


18 


332 


6 


129 


17 


326 


6 


146 


17 


319 


7 


162 


16 


311 


8 


178 


16 


302 


9 


194 


16 


292 


10 


209 


16 


281 


11 


224 


16 


270 


. U 




14 




13 


+238 




+258 




251 


+13 


245 


-13 


263 


13 


232 


18 


+275 


+13 

■ 


+218 


-14 



Ci 



+ 6 

7 
8 
9 
9 

10 
10 
11 
11 
11 

11 

+11 



65 



TABLE lY .—GmOimed. 

PERTUBBATIONS OF THE CX)-OBDINATES IN UNITS OF THE SIXTH DECIMAL. 

AKGUMENT VHL 



Aig. 

o 
138 

141 

144 

147 

150 

153 

156 

159 

162 

165 

168 
171 
174 
177 
180 
183 
186 
189 
192 
195 

198 
201 
204 
207 
210 
213 
216 
219 
222 
225 

228 
231 
234 
237 

240 
243 
246 
249 



+275 
286 
297 
306 
315 
322 
329 
335 
340 
344 

+348 
350 
351 
352 
351 
349 
347 
343 
339 
334 

+327 
320 
312 
303 
294 
283 
272 
260 
247 
233 

+219 
205 
189 
173 
157 
141 
124 

+106 



Diff. 



+11 
11 
9 
9 
7 
7 

e 

6 

4 

4 

+ 3 
1 
+ 1 
- 1 
9 
9 
4 
4 
6 



7 
8 
9 
9 

• 

11 
11 
13 
18 
U 

14 

■14 
16 
16 
16 
16 
17 
•18 



+218 

203 
188 
172 
156 
139 
122 
105 
87 
69 

+ 51 

33 

+ 15 

- 3 

22 

40 

58 

76 

94 

112 

-129 
146 
162 
178 
194 
209 
223 
237 
250 
263 

-275 
286 
296 
305 
314 
322 
329 

-335 



Diff. 



-15 
16 
16 
16 
17 
17 
17 
18 
16 

18 

-18 
18 
18 
19 
18 
18 
18 
18 
18 

IT 

-17 
16 
16 
16 
16 
14 
14 
18 
It 

19 

-11 
10 
9 
9 
8 
7 

- 6 



+11 
11 
11 
10 

9 

9 
8 
7 
6 
5 

4 

3 
2 

+ 1 


- 2 
3 
4 

- 5 



Aig. 

o 
249 

252 

255 

258 
261 
264 
267 
270 
273 
276 

279 
282 
285 
288 
'291 
294 
297 
300 
303 
306 

309 
312 
315 
318 
321 
324 
327 
330 
333 
336 

339 
342 
345 
348 
351 
354 
357 
360 



+106 
89 
71 
53 
34 
+ 16 
- 3 
21 
39 
58 

-76 
94 
111 
129 
146 
162 
178 
194 
209 
224 

-238 
251 
264 
276 
287 
297 
306 
315 
323 
330 

-336 
341 
345 
348 
351 
352 
352 

-352 



Diff. 



■17 

18 
18 
19 
18 
19 
18 
18 
19 

18 

-18 
17 
18 
17 
16 
16 
16 
16 
16 

14 

-18 

18 

13 

11 

10 

9 

9 

8 

7 



6 

4 
8 
8 
1 





-335 
340 
344 
347 
349 
350 
351 
350 
349 
346 

-342 
338 
333 
326 
319 
311 
302 
292 
282 
271 

-259 
246 
232 
218 
203 
188 
173 
156 
140 
123 

-106 

87 

70 

51 

33 

- 15 

+ 4 

+ 22 



Diff. 



- 6 
4 
8 
3 
1 

- 1 

+ 1 

• 
1 

8 



+ 4 

6 

7 

7 

8 

9 

10 

10 

11 

13 

+18 
14 
14 
16 
16 
16 
17 
16 
17 

18 

+18 
17 
19 
18 
18 
19 

+18 



-6 

7 
8 
9 
9 

10 
10 
11 
11 
11 

11 
11 

11 

« 
11 

10 

» 
9 

8 
+ 7 



66 



TABLE lY.—Cbniinued. 

PERTURBATIONS OF THE CO-ORDINATES IN UNITS OP THE SIXTH DECIMAL. 

AHGUlfENT IX. 



Arg. 



100 
105 
110 

lis 
lao 

*125 
130 
135 
140 
145 

150 
155 
160 
165 
170 
175 
180 






+150 


5 


150 


10 


150 


15 


151 


20 


152 


^ 


153 


30 


153 


.35 


.153 


40 


153 


45 


152 


50 


+149 


55 


146 


60 


141 


65 


134 


70 


126 


75 


116 


80 


104 


85 


89 


90 


72 


95 


53 



+ 31 

+ 7 

- 18 

45 

73 

101 

130 

159 

186 

212 

-236 
257 
274 

288 

298 

304 

-305 



Diff. 






+ 1 
1 

+ 1 





- 1 



- 8 
6 
7 
8 

10 
13 
15 
17 
19 

-34 
36 
37 
38 
38 
39 
39 
37 
36 

34 

-31 

17 

14 

10 

6 

- 1 



ni 



- 3 
11 
18 
26 
34 
43 
53 
63 
75 
87 

-100 
114 
128 
143 
158 
173 
188 
202 
216 
228 

-238 
246 
252 
255 
255 
251 
243 
232 
217 
198 

-176 

150 

121 

90 

58 

- 24 
+ 11 



Diff. 



- 8 
7 
8 
8 
9 

10 
10 
13 
13 

18 

-14 
14 
Iff 
16 
IS 
16 
14 
14 

13 

• 

10 

- 8 
8 

- 8 


+ 4 

8 
11 
16 
19 

33 

+36 
39 
81 
83 
84 

+86 



ii 



+22 

20 

18 

16 

13 

11 

8 

6 

+ 3 



- 2 

5 
8 
10 
13 
16 
18 
20 
23 
25 

-27 

28 
30 
31 
32 
33 
34 
34 
34 
34 

-33 
32 
31 
29 
28 
26 

-24 



Arg. 



180 
185 
190 
195 
200 
205 
210 
215 
220 
225 

230 
235 
240 
245 
^0 
255 
260 
265 
270 
275 

280 
285 
290 
295 
300 
305 
310 
315 
320 
325 

330 
335 
340 
345 
350 
355 
360 



h 



-305 
302 
294 
282 
267 
247 
225 
200 
172 
144 

-115 
86 
57 
29 
- 3 
+ 22 
45 
65 
83 
99 

+113 
124 
132 
139 
144 
148 
150 
152 
152 
15^ 

+152 
151 
150 
150 
150 
149 

+150 



Diff. 



+ 8 
8 
13 
16 
30 
93 
36 



39 

+39 
39 
38 
36 
36 
38 
30 
18 
16 

14 

+11 
8 
7 
6 
4 
3 

+ 3 





- 1 
1 




- 1 

+ 1 



m 



+ 11 

45 
78 
110 
140 
167 
192 
212 
230 
243 

+252 
257 
259 
257 
252 
244 
234 
222 
209 
194 

+178 

163 

147 

131 

116 

102 

69 

76 

64 

54 

+ 44 
35 
27 
19 
11 
+ 4 
- 3 



Diff. 



+84 
88 
83 
80 
37 
36 
SO 
18 
18 

9 

+ 6 
+ 3 

- 3 
6 
8 

10 
13 
18 
16 

16 

-16 
16 
16 
16 
14 
18 
IS 
13 
10 

10 

- 9 
8 
8 
8 
7 

- 7 



ii 



-24 

21 

19 

16 

13 

10 

7 

4 

- 1 

+ 2 

+ 5 
8 
11 
13 
16 
18 
21 
23 
25 
26 

+28 
29 
30 
31 
31 
32 
32 
32 
31 
31 

+30 
29 

' 28 
27 
25 
24 

+22 



J 



67 



TABLE lY .—Continued. 

PERTURBATIONS OP THE COORDINATES IN UNITS OP THE SIXTH DECIMAL. 

ABGUMENT X. 



Arg. 



o 


. 6 

10 

15 

20 

25 

30 

35 

40 

45 

50 
55 
60 
65 
70 
75 
80 
85 
90 
95 

100 
105 
110 
115 
120 
125 
130 
135 
140 
145 

150 
155 
160 
165 
170 
175 
180 



+187 
186 
183 
178 
172 
164 
155 
145 
133 
121 

+107 
92 
77 
61 
45 
28 

+ 11 

- 6 
23 
39 

- 55 
71 
86 

100 
113 
125 
136 
146 
155 
163 

-169 
174 
177 
179 
180 
180 

-178 



Diff. 


ni 


Diff. 


& 




- 10 




+ 6 


- 1 


26 


-7l6 


5 


8 


43 


17 


4 


ff 


60 


17 


3 


6 


76 


16 


3 


8 


91 


16 


2 


9 


106 


16 


+ 1 


10 


120 


14 





13 


133 


18 


- 1 


13 


145 


13 


2 


14 




11 






-156 




- 3 


-15 


165 


- 


4 


16 


173 


8 


5 


16 


180 


7 


6 


16 


185 


6 


7 


17 


188 


8 


7 


17 


190 


3 


8 • 


17 


191 


- 1 


9 


17 


189 


+ 3 


9 


16 


187 


3 


10 


16 




4 






-183 




-10 


-16 


177 


+ 6 


10 


16 


170 


7 


11 


14 


162 


8 


11 


13 


152 


10 


11 


13 


141 


11 


11 


11 


130 


11 


11 


10 


117 


18 


11 


9 


104 


18 


10 


8 


90 


14 


10 


6 




15 






- 75 




-10 


- 6 


60 


+15 


9 


8 


45 


IS 


9 


3 


29 


16 


8 


- 1 


- 14 


15 


7 





+ 2 


16 


7 


+ 3 




+16 






+ 17 




- 6 



Arg. 



180 
185 
190 
195 
200 
205 
210 
215 
220 
225 

230 
235 
240 
245 
250 
255 
260 
265 
270 
275 

280 
285 
290 
295 
300 
305 
310 
315 
320 
325 

330 
335 
340 
345 
350 
355 
360 



-178 
175 
171 
166 
159 
152 
143 
134 
123 
112 

-100 
87 
74 
60 
46 
32 
17 
- 2 
+ 14 
29 

+ 44 

59 

73 

87 

101 

114 

126 

138 

148 

158 

+166 
173 
179 
183 
186 
187 

+187 



Diff. 


th 


Diff. 




+ 17 




+ 8 


33 


+16 




48 


16 




62 


14 




76 


14 




90 


14 




103 


18 




115 


13 




126 


11 




136 


10 
10 




+146 




+18 


154 


+ 8 




162 


8 




168 


6 




173 


6 




177 


4 




180 


3 




181 


1 

1 . 




182 


+ 1 




180 


- 3 

3 




+178 




+16 


174 


- 4 




169 


5 




163 


6 




156 


7 




147 





13 


137 


10 


13 


126 


11 


10 


114 


13 


10 


101 


18 


8 


+ 87 


14 


+ 7 


72 


-16 


6 


57 


16 


4 


41 


16 


8 


24 


17 


+ 1 


+ 7 


17 





- 10 


-17 



- 6 
5 
4 
3 
2 
2 

- 1 


+ 1 
2 

+ 3 
4 

5 
6 
6 

7 
8 
8 
9 
9 

+10 
10 
11 
11 
11 
11 
11 
11 
11 
10 

+10 
9 
9 
8 
8 
7 

+ 6 



68 



TABLE IV.—CotOintted. 

PERTURBATIONS OF THE CXM)RDINATES IN UNITS OF THE SIXTH DECIMAL. 



ARQUUEIirr ZI. 



Ai^. 


h 


Diff. 


m 


Diff. 


Ci 


Aig. 


h 


Diff. 


^1 


Diff. 


1 <- 


o 


•5 
10 
15 


+101 

08 
92 
83 


- s 

6 
9 


+ 11 

30 
48 
65 


+19 


- 3 

- 1 
+ 1 

2 



180 

185 

190 

195 


-144 
144 
144 
145 






- 1 


+ 10 
8 
6 

+ 3 


- 3 


-30 
31 
31 
32 


20 


72 


11 


79 




3 


200 


145 










32 


25 
30 


58 
43 


14 
1« 


92 
102 




4 

4 


.205 
210 


145 
146 




- 1 


- 3 
6 




33 
34 


35 


27 


18 


110 




4 


215 


146 





10 




34 


40 


+ 11 


16 


116 




4 


220 


146 





14 


* 


35 


45 


- 5 


18 
16 


119 


+ 1 


3 


225 


146 




+ 1 


18. 




• 36 


50 
55 


- 21 
36 


-16 


+120 
119 


- 1 


+ 2 
+ 1 


230 
235 


-145 
144 


+ 1 


-23 

28 


- 6 


-36 
37 


60 


51 


1ft 


117 







240 


142 


3 


34 




37 


65 


64 


IS 


114 




-2 


245 


140 


3 


41 




37 


70 


76 


13 


110 




3 


250 


137 


8 


47 




38 


75 


87 


11 


105 




5 


255 


133 


4 


54 




38 


80 


97 


10 


99 




7 


260 


128 


6 


61 




38 


85 


106 


9 


93 




9 


265 


122 


6 


69 




38 


90 


113 


7 


86 




10 


270 


115 


7 


76 




38 


05 


120 


7 
6 


80 




12 


275 


106 


9 
9 


83 




37 


100 
105 


-125 
130 


- 6 


+ 73 
67 


- 6 


-14 
15 


280 
285 


- 97 
86 


+11 


- 90 
96 


— 6 


36 


110 


133 


8 


61 




17 


290 


74 


13 


101 




35 


115 


136 


8 


55 




18 


295 


60 


14 


106 




34 


120 
125 


139 
140 


8 
1 


49 
44 


• 


19 
21 


300 
305 


46 
30 


14 
16 


109 
111 


- 3 


32 
30 


130 


141 


1 


40 




22 


310 


- 13 


♦ " 


111 


+ 8 


28 


135 


142 


1 


36 




23 


315 


+ 4 


17 


108 


26 


140 


143 


1 


32 




24 


320 


21 


17 


103 




24 


145 


143 






29 




25 


325 


38 


17 
16 


96 




21 


150 
155 


-143 
143 


- 


+ 26 
23 


— 8 


-26 

26 


330 
335 


+ 54 
68 


+14 


- 87 
75 


+13 


-19 
16 


160 


143 





20 




27 


340 


80 


13 


60 


16 


13 


165 


143 





18 




28 


345 


90 


10 


44 


16 


10 


170 
175 
180 


143 

144 

-144 




- 1 




15 

13 

+ 10 


— 8 


29 

29 

-30 


350 
355 
360 


97 

101 

+101 


7 

+ 4 




26 
- 7 
+ 11 


18 

19 

+18 


8 

5 

- 3 



69 







• 

TABLE lY.—Cimlinued. 




PERTURBATIONS OP THE COORDINATES IN UNITS OP THE 


, SIXTH DECIMAL. 






ARGUMENT XXL 




Arg. 


• 


Diff. 


Vl 


Diff. 


Cl 


Aig. 


6 


Diff. 


Vi 


Diff. 


Ci 


o 



-97 




- 6 




-2 


o 
180 


+122 




+ 8 




+2 


5 


96 


+ 1 


13 


MW 1 




185 


120 


- a 


20 


+13 




10 


95 


1 

4 


21 




2 


190 


117 


8 


31 




2 


15 


94 


1 

4k 


28 






195 


114 


8 


42 






20 


92 


9 


35 




3 


200 


109 


5 


52 




3 


25 


89 


S 


43 




• 


205 


103 


6 


62 






30 


86 


s 


50 




3 


210 


96 


7 


71 




3 


35 


82 


4 


57 






215 


88 


8 


79 






40 


78 


4 


64 




2 


220 


80 


8 


86 




2 


45 


74 


4 
6 


70 






225 


71 



10 


93 






50 


-68 




- 77 




2 


230 


+ 61 




+ 96 




2 


55 


62 


+ « 


83 


^ 6 




235 


51 


-10 


103 


+ 6 




60 


66 


6 


88 




2 


240 


41 


10 


106 




2 


65 


49 


7 


93 






245 


31 


10 


109 






70 


41 


8 


96 




2 


250 


20 


11 


110 


A m 


2 


75 


33 


8 


102 






255 


+ 10 


10 


111 


+ 1 




80 


24 


9 


105 




1 


260 





10 


110 


"* 1 


1 


85 


15 


9 


108 






265 


- 10 


10 


109 






90 


- 5 


10 


109 




1 


270 


19 


9 


107 




1 


95 


+ 5 


10 
10 


110 




• 


275 


29 


10 

8 


104 






100 


+ 15 




-110 




-1 


280 


- 37 




+100 




+1 


105 


25 


+10 


109 


+ 1 




285 


45 


- 8 


96 


"" 4 




no 


36 


11 


107 







290 


53 


8 


91 







115 


46 


10 


105 






295 


60 


7 


86 






120 


56 


10 


101 







300 


66 


6 


80 







125 


66 


10 


96 






305 


72 


6 


74 






130 


75 





90 




+1 


310 


77 


5 


67 




-1 


135 


84 


9 


83 






315 


81 


4 


60 






140 


92 


8 


75 




1 


320 


85 


4 


53 




1 


145 


99 


7 
7 


66 






325 


88 


8 
8 


46 






150 


+106 




- 57 




1 


330 


- 91 




+ 39 




1 


155 


111 


+ 6 


47 


+10 




335 


93 


- 3 


32 


^^ I 




160 


115 


4 


37 


10 


2 


340 


95 


3 


24 




2 


165 


119 


4 


26 


11 




345 


96 


1 


17 






170 


121 


3 

+ 1 


15 


11 


2 


350 


97 


- 1 


9 


A 


2 


175 


122 


- 3 


13 




355 


97 





+ 2 






180 


+122 





+ 8 


+11 


+2 


360 


- 97 





- 6 


- 8 


-2 






70 



PERT 


UKBAT] 


[0N8 C 


1 

>F THE 


1 

TABLE lY .^ebiOmued. 




1 SIXTH 


: DECI 


MAL. 


CO-ORDINATES IN UNITS OF THE 










ARGUMENT XTH. 








Ai^. . 


h 


Diff. 


Vi 


DiflF. 


ii 


Ai^. 


h 


I>iff. 


Vi 


Biff. 


Ci 


o 



-83 









- 6 


o 
180 


+83 




+ 




+ 6 


5 


82 


+1 


- 4 


-4 




185 


82 


-1 


3 


+8 




10 


80 


3 


7 


S 


4 


190 


80 


3 

4% 


7 


4 


4 


15 


78 


3 


11 


4 




195 


78 


3 


10 


8 




20 


75 




14 


8 


- 2 


200 


75 




14 


4 


+ 2 


25 


72 




17 


S 




■205 


71 




. 17 


8 




30 


68 




21 


4 





210 


67 




20 


8 





35 


63 




24 


S 




215 


62 




23 


8 




40 


58 




26 


3 


+ 1 


220 


57 




26 


8 


- 1 


45 


52 




^ 


S 




225 


52 




28 


3 




50 


-46 




-31 


3 


3 


230 


+46 




+31 


8 


3 


55 


40 


+6 


33 


-3 




235 


39 


-7 


33 


+3 

4k 




60 


33 




35 


3 


5 


240 


33 




35 


3 


5 


65 


26 




37 


3 




245 


26 




36 


1 




70 


19 




38 


1 


7 


250 


19 




38 


3 

m 


7 


75 


12 




39 


1 




255 


12 




39 


1 




80 


- 5 




40 


-1 


8 


260 


+ 5 




40 


+1 


8 


85 


+ 3 




40 







265 


- 3 




40 







90 


10 




40 





9 


270 


10 




40 





9 


95 


17 




40 




+1 




275 


17 




40 







100 


+24 




-39 


, 


10 


380 


-24 




+40 




10 


105 


31 


+7 


39 


+0 




285 


31 


-^ 


39 


^** 1 




110 


38 




38 


1 


10 


290 


38 




38 




10 


115 


44 




36 


3 




295 


44 




37 






120 


50 




34 


3 


11 


300 


50 




35 


4^ 


11 


125 


66 




32 


3 




305 


56 




33 


3 




130 


61 




30 


3 


11 


310 


61 




31 


3 


11 


135 


66 




28 


3 




315 


66 




29 


3 




140 


70 




25 


8 


10 


320 


70 




26 




10 


145 


74 




23 


3 




325 


74 




23 






150 


+77 




-20 


9 


9 


330 


-77 




+20 




9 


155 


80 


+» 


17 


+8 




335 


80 


"• 


17 


^**o 




160 


82 




13 


4 


8 


340 


82 




14 




8 


165 


83 




10 


8 




345 


83 


• 


10 






170 


• 84 


+1 


7 


8 


7 


350 


84 


j^ 


7 




7 


175 


84 





- 3 


4 




355 


84 





+ 3 






180 


+83 


-1 





+8 


+ 6 


860 


-83 


+1 







-6 





71 





• 




TABLE IV, Omfinued. 








PERTURBATIONS OP THE COORDINATES IN UNITS OP THE SIXTB 


DECIMAL. 1 








ARGUMENT XTV. 








Arg. 


h 


Diff. 


^1 


Diff. 


il 


Arg. 


h 


Diff. 


Vi 


Diff. 


(l 


o 



+44 




+ 3 




+2 


o 
180 


-54 




- 2 




-2 


5 


45 


+1 


- 1 


^^A 




185 


54 





+ 3 


+6 




10 


45 





4 




2 


190 


54 




1 m 


8 




2 


15 


44 


-I 


7 






195 


53 


+ 1 


13 






20 


44 





11 




1 


200 


51 


3 


18 




1 


25 


43 


1 


14 






205 


49 


3 


23 






30 


42 


1 


18 




+1 


210 


47 


3 


27 




-1 


35 


* 41 


1 


21 






215 


44 


8 


31 






40 


39 


% 


24 







220 


40 


4 f 


35 







45 


37 


3 


28 






225 


37 


8 

4 


38 






50 


+35 


3 


-31 




-1 


830 


-33 


4 


+41 




+1 


55 


32 


-8 


34 


**8 




235 


29 


+4 


44 


+8 




60 


30 


9 


37 




1 


240 


24 


6 

M 


46 




1 


65 


27 




40 






245 


20 


4 


47 






70 


23 




42 


3 


9 


250 


15 


6 


48 




2 


75 


20 




44 


9 




255 


11 


4 


49 


i - 




80 


16 




46 


3 


2 


260 


6 


6 


60 


+1 


2 


85 


12 




48 






265 


-2 


4 


49 






90 


8 




49 




3 


270 


+ 2 


4 


49 




3 


95 


+ 3 




50 






275 


7 


6 


48 






100 


- 1 




-51 




3 


280 


+11 


4 


+47 




8 


105 


6 


^"O 


51 






285 


14 


+8 


45 


-3 




110 


11 




51 


1 . 


3 


290 


18 


4 


44 




3 


115 


15 




50 


+1 




295 


22 


4 


42 






120 


20 




49 




3 


300 


25 


8 


39 




3 


125 


25 




47 






305 


28 


8 


37 






130 


29 




45 




4 


310 


30 


3 


34 




4 


135 


33 




42 






315 


33 


8 


31 






140 


37 




39 




3 


820 


35 


3 


28 


• 


3 


145 


41 




35 






325 


37 


3 
3 


25 






150 


-44 




-31 




3 


830 


+39 




+22 




3 


155 


47 


-s 


27 


+4 




335 


40 


+1 


19 


^**o 




160 


60 




23 




3 


840 


42 


3 


16 




3 


165 


52 




18 






345 


43 


1 


13* 






170 


53 




13 




8 


350 


43 





10 




3 


175 


54 


—"1 


8 






355 


44 


+ 1 


6 






180 -54 





- 2 


+0 


-2 


860 


+44 




• 


+ 3 




+2 










• 

















72 



TABLE ly.—Omiinued. 

PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. 

ARGUMENT XV. 



Arg. 




5 
10 
15 
20 
25 
30 
35 
40 
45 

50 
55 
60 
65 
70 
75 
80 
85 
90 
95 

100 
105 
110 
115 
120 
125 
130 
135 
140 
145 

150 
155 
160 
165 
170 
175 
180 



-29 
29 
29 
28 
27 
26 
25 
23 
22 
20 

-18 

16 

14 

11 

9 

7 

4 

- 1 

+ 1 

4 

+ 6 
9 
12 
14 
16 
19 
21 
23 
25 
26 

+28 
29 
30 
30 
31 
31 

+31 



Diff. 






+1 
1 
I 
1 

3 
1 
2 



+3 
3 
8 
3 
3 
3 
8 
3 
8 

3 

+8 
8 

3 
3 
8 
3 
3 
3 
1 

3 

+1 
1 


+1 





Vi 



- 2 

4 

7 

9 

12 

14 

16 

18 

20 

22 

-24 
25 
26 
27 
28 
29 
30 
30 
30 
30 

-30 
29 
28 
27 
26 
24 
23 
21 
19 
16 

-14 

11 

9 

6 

3 

- 1 

+ 2 



Diff. 



-3 
3 
3 
8 
3 
2 
3 
3 
3 









+1 
1 
1 
1 
3 
1 
3 
3 
8 

3 

+8 
3 
8 
8 
3 

+8 














































Aig. 



180 
185 
190 
195 
200 
205 
210 
215 
220 
225 

230 
235 
240 
245 
250 
255 
260 
265 
270 
275 

280 
285 
290 
295 
300 
305 
310 
315 
320 
325 

330 
335 
340 
345 
350 
355 
360 



+31 
31 
30 
29 
28 
27 
25 
24 
22 
20 

+18 

15 

13 

10 

8 

5 

+ 2 



- 3 
5 

- 8 
10 
13 
15 
17 
19 
21 
23 
24 
25 

-27 

28 
28 
29 
29 
29 
-29 



Diff. 





-I 
1 
1 
1 

3 
1 
3 
3 

3 

-8 
3 
8 
3 
8 
8 
3 
8 
3 

8 

-3 
8 

3 
3 
3 
3 
3 
1 
1 

3 

-1 


-1 






Vl 



+ 2 
5 
7 
10 
13 
15 
17 
20 
22 
23 

+25 
26 
28 
29 
29 
30 
30 
30 
30 
30 

+29 
28 
27 
26 
24 
23 
21 
19 
17 
15 

+13 

10 

8 

6 

3 

+ 1 

- 2 



Diff. 



+3 
3 
8 
3 
3 
3 
8 
3 
1 

3 

+1 
3 
1 


+1 





-1 

-1 
1 
I 

3 
1 
3 
3 
3 
3 



•8 

3 
3 
8 
3 
-8 















































73 



TABLE lY. —Cbntinued. 




PERTURBATIONS OF THE COORDINATES IN UNITS OF THE SIXTH DECIMAL. 


ARGUMENT XVI. 


ABGUMENT XVH. 


Arg. 


h 


Diff. 


^1 


DiflF. 


il 


Aig. 


h 


Diff. 


ni 


Diff. 


Ci 


o 



+113 


* 


+ 4 




+2 


o 



-103 




- 16 




-2 


5 


113 





- 6 


-10 




5 


102 


+1 


24 


-8 




10 


112 


- 1 


15 


9 


2 


10 


99 




33 




2 


15 


110 


3 


25 


10 




15 


96 




42 






20 


108 


3 


34 




1 


20 


92 




50 




1 


25 


104 


4 


43 






25 


87 




57 




. 


30 


100 


'4 


52 




+1 


30 


82 




64 




-1 


35 


95 


6 


61 






35 


76 




71 






40 


89 


6 


69 







40 


69 




78 







45 


83 


6 

7 


76 






45 


62 




83 






50 


+ 76 




- 83 







50 


-54 




-88 







55 


68 


- 8 


89 


"* H 




55 


46 


+8 


93 


^^O 




60 


60 


8 


95 




-1 


60 


38 




96 




+1 


65 


52 


8 


100 






65 


29 


• j^ 


99 






70 


43 


9 


104 




1 


70 


20 




101 


3 


1 


75 


34 


9 


107 






75 


11 


\ 


103 


—3 




80 


24 


10 


110 




2 


80 


- 2 




103 





1 


85 


14 


10 


111 






85 


+ 7 




103 







90 


+ 5 


9 


112 


"^ 1 


2 


90 


16 




102 


+1 


2 


95 


- 5 


10 
10 ' 


112 


+ 1 




95 


25 




101 






100 


- 15 




-111 




3 


100 


+ 34 




- 98 




2 


105 


25 


-10 


109 


+ 3 




105 


42 


+8 


95 


+8 




110 


34 


9 


107 




3 


110 


50 




91 




2 


115 


43 


9 


103 






115 


58 




86 






120 


52 


9 


99 




3 


120 


66 




81 




2 


125 


61 


9 


94 






125 


73 




75 






130 


69 


8 


88 




3 


130 


79 




68 




2 


135 


77 


8 


82 






135 


85 




61 






140 


84 


7 


75 




3 


140 


90 




54 




3 


145 


90 


6 
6 


68 






145 


94 




46 


8 
8 




150 


- 95 




-60 




3 


150 


+ 96 




- 38 




2 


155 


100 


- 6 


51 


+ 9 




155 


101 


+8 


29 


+9 




160 


105 


5 


42 




3 


160 


103 




20 


9 


2 


165 


108 


3 


33 






165 


104 


1 . 


11 


9 




170 


110 


3 


24 




2 


170 


105 


+1 


- 2 


9 


2 


175 


112 


3 


14 


10 




175 


104 


"* 


+ 7 


9 




180 


-113 


- 1 


- 4 


+10 


-2 


180 


+103 




+ 16 


+9 


+2 


180^ are to be subtracted from the ArgameDts > 180^, and h* m* A>^d ti to be taken with the reyc 


snedsi^. 





10 



74 





TABLE lY.—Cbniinued. 


PEETUBBATIONS OP THE CXMDEDINATES IN UNITS OP THE SIXTH DECIMAL. 


ARGUMENT XYIIL 


ARGUMENT XIX. 


Aig. 


h 


Diff. 


ni 


Diff. 


Ci 


Aig. 


ii 


Diff. 


Vi 


Diff. 


Cl 


O 




+43 




+ 5 


I ^ 





o 




+29 




+14 


t M 


-1 


10 


41 


—3 


12 


+7 





10 


26 


"■ 


18 


+4 


-1 


20 


39 


9 


19 


7 





20 


22 




22 


4 





30 


35 


4 


26 


7 





30 


17 




26 


4 





40 
50 


30 
24 


6 
6 


31 
36 


6 
6 






40 
50 


12 

7 




28 
30 


3 

+3 




+1 


60 


17 


7 


40 


4 





60 


+ 1 




30 





1 


70 
80 


10 
+ 3 


7 
7 


42 
43 


3 

+1 






70 
80 


- 5 
10 




30 
29 



-1 


1 

2 


90 


- 5 


8 


43 








90 


15 




27 


3 


2 


100 
110 


-12 
19 


7 
-7 


+42 
39 


1 

-8 






100 
110 


-20 
24 


—4 


+24 
21 


8 
-8 


+2 
2 


120 
130 


26 
31 


7 
6 


36 
30 


4 

6 






120 

130 


28 

30 


3 


17 
12 


4 
6 


2 
2 


140 


36 


6 


24 


8 





140 


32 


3 


7 


6 


2 


150 
160 

170 
180 


39 

42 

43 

-43 


S 

8 

-1 




17- 

10 
+ 3 
- 5 


7 

7 

7 

-8 








150 

160 
170 
180 


33 

33 

31 

-29 


—1 



+3 

+3 


+ 2 

- 4 

9 

-14 


6 

6 

6 

-6 


1 
1 

1 


ARGUMENT XX. 


ARGUMENT XXI. 


ARGUMENT XXTT. 


Ai^. 


€i 


Vi 


Ci 


Arg. 


fe 


m 


Ci 


Aig. 


6 


m 


Ci 


o 



-27 


- 4 





o 



+25 


+ 1 





o 



-24 


+10 


1 

-8 


10 


26 


9 





10 


24 


- 3 





10 


21 


14 


8 


20 


24 


13 





20 


24 


8 





20 


17 


18 


8 


30 


21 


17 





30 


22 


12 





30 


13 


21 


7 


40 


18 


21 





40 


20 


16 





40 


9 


23 


7 


50 


14 


23 





50 


17 


19 





50 


- 4 


25 


6 


60 


10 


25 





60 


13 


22 





60 


+ i 


26 


5 


70 


- 5 


27 





70 


10 


24 





70 


6 


26 


3 


80 





27 





80 


6 


26 





80 


10 


25 


2 


90 


+ 4 


27 





90 


+ 1 


26 





90 


15 


23 


-1 


100 


+ 9 


-26 





100 


- 3 


-26 





100 


+19 


+21 


+1 


110 


13 


24 





110 


7 


25 





110 


22 


19 


2 


120 


17 


21 





120 


11 


24 





120 


25 


15 


4 


130 


21 


18 





130 


15 


21 





130 


26 


11 


5 


140 


23 


14 





140 


18 


18 





140 


28 


7 


6 


150 


25 


10 





150 


21 


14 





150 


28 


+ 3 


7 


160 


27 


- 5 





160 


23 


10 





160 


27 


-2 


8 


170 


27 








170 


24 


6 





170 


26 


6 


8. 


180 


+27 


+ 4 





180 


-25 


- 1 





180 


+24 


tIO 


+8 


180^ are to be Bubtracted from the Alignments > 180^, and h, nif ab^ ^ to be taken with the reversed sign. 



75 



TABLE lY.—CbnUnued 

PERTURBATIONS OF THE COORDINATES IN UNITS OP THE SIXTH DECIMAL. 



ARGUMENT XXWL 



Aig. 




10 



30 
40 
50 
60 
70 
80 
90 

100 
110 
120 
130 
140 
150 
160 
170 
180 



-22 
22 
21 
20 
18 
15 
12 
9 
5 

- 1 

+ 3 
6 
10 
13 
16 
18 
20 
22 

+22 



ni 



- 2 
+ 2 
6 
10 
13 
16 
18 
20 
21 
22 

-H22 

21 

20 

18 

15 

12 

9 

5 

+ 2 



-1 
1 

-1 





+1 
1 
1 

+1 
1 

2 
2 
2 
2 
1 
1 
+1 



ARGUMENT XXIV. 



Axg, 



o 


10 

20 

30 

40 

50 

60 

70 

80 

90 

100 
110 
120 
130 
140 
150 
160 
170 
180 



+20 

20 

18 

16 

14 

11 

8 

+ 4 



- 3 

- 7 
10 
13 
16 
18 
19 
20 
21 

-20 



Vi 



-4 

4 
4 
3 
3 
2 
1 

-1 


+1 

+1 
2 
3 
3 
4 
4 
4 
4 

+4 



+2 
1 

+1 


-1 
2 
2 
3 
4 
4 



4 

4 
4 
4 
4 
8 
3 
-2 



ARGUMENT XXV. 



Aig. 




10 
20 
30 
40 
50 
60 
70 
80 
90 

100 
110 
120 
130 
140 
150 
160 
170 
180 



-19 

19 

18 

16 

14 

12 

9 

6 

- 3 

+ 1 

+ 4 
7 
10 
13 
15 
17 
18 
19 

+19 



^ 



+ 1 
4 
7 
10 
13 
15 
17 
18 
19 
19 

+19 

18 

16 

14 

12 

9 

6 

+ 3 

- 1 



Ci 


























ARGUMENT XXVL 



Arg. 




10 
20 
30 
40 
50 
60 
70 
80 
90 

100 
110 
120 
130 
140 
150 
160 
170 
180 



+19 
21 
23 
24 
24 
23 
22 
20 
17 
14 

+11 

7 

+ 3 

- 1 

6 

10 

13 

16 

-19 



ni 



+13 

9 

6 

+ 2 

- 2 

6 

10 

13 

16 

19 

-21 
22 
23 
23 
22 
20 
18 
16 

-13 


























ARGUMENT XXVIL 



Aig. 




10 
20 
30 
40 
50 
60 
70 
80 
90 

100 
110 
120 
130 

140 
150 
160 
170 
180 



+16 

14 

12 

10 

7 

4 

+ 1 

- 3 

6 

9 

-n 

14 
16 
17 
18 
18 
18 
17 
-16 



^1 



+11 

7 

+ 2 

- 2 

7 

11 

15 

19 

22 

24 

-25 
26 
26 
25 
24 
21 
19 
15 

-11 



+3 
3 
3 
2 
2 
2 
1 

+1 



-1 
1 
2 
2 
8 
8 
8 
3 

-3 



ARGUMENT XXVIII. 



Arg. 



o 


10 

20 

30 

40 

50 

60 

70 

80 

90 

100 
110 
120 
130 
140 
150 
160 
170 
180 



-15 
14 
13 

19 

10 
8 
6 

- 3 


+ 2 

+ 5 

7 

9 

11 

13 

14 

15 

15 

+15 



% 



+ 5 
8 
11 
14 
16 
18 
19 
20 
19 
19 

+18 

16 

14 

11 

8 

5 

+ 2 

- 2 

- 5 



+1 
1 
1 

+1 





-1 
1 

-1 
1 
1 

2 
2 
2 
2 
2 
-1 



180^ are to be sabtracted from the Arguments > 180^, and ^i, m, mmL Ci to be taken with the rerersed sign. 



76 



TABLE lY.—Cbtitimed. 

PERTURBATIONS OF THE COORDINATES IN UNITS OF THE SIXTH DECIMAL, 



ARGUMENT XXTX. 



Aig. 



o 


10 

20 

30 

40 

50 

60 

70 

80 

90 

100 
110 
120 
130 
140 
150 
160 
170 
180 



h 


ni 


+12 


+ 1 


12 


- 1 


12 


3 


11 


5 


10 


7 


9 


9 


7 


10 


5 


11 


3 


12 


+ 1 


12 


- 1 


-12 


3 


' 12 


5 


11 


7 


10 


9 


9 


10 


7 


11 


5 


12 


3 


-12 


- 1 



Cl 





















ARGUMENT XXX. 



Arg. 




10 
20 
30 
40 
50 
60 
70 
80 
90 

100 
110 
120 
130 
140 
150 
160 
170 
180 



-8 
8 
7 
7 
6 
5 
4 
2 
-1 
+1 

+2 
3 
4 
5 
6 
7 
8 
8 

+8 



Vi 



-1 
2 
3 

5 
6 

7 
8 
8 
8 
8 

-8 
8 
7 
6 
5 
4 
2 
-1 
+1 



























ARGUMENT XXXL 



Arg. 




10 
20 
30 
40 
50 
60 
70 
80 
90 

100 
110 
120 
130 
140 
150 
160 
170 
180 



-7 
7 
6 
6 
5 
4 
3 

-2 


+1 

+2 
3 
4 
5 
6 
7 
7 
7 

+7 



ni 



-1 

2 
3 
4 

5 
6 
6 
7 
7 
7 

-6 
6 
5 
5 
4 
3 

-2 


+1 



ARGUMENT XXXH. 



Arg. 




10 
20 
30 
40 
50 
60 
70 
80 
90 

100 
110 
120 
130 
140 
150 
160 
170 
180 



+4 
5 
6 
6 
7 
7 
7 
6 
6 
5 

+4 
3 
2 

+1 


-1 
2 
3 

-4 



^1 



-6 
4 

3 

. 2 

-1 



+1 
2 
3 
4 

+5 
5 
6 
6 
6 
6 
6 
5 



Ci 


























ARGUMENT XXXIIL 



Aig. 




10 
20 
30 
40 
50 
60 
70 
60 
90 

100 
110 
120 
130 
140 
150 
160 
170 
180 



+3 
3 
3 
3 
3 
2 
2 
1 

+1 



-1 
1 
2 
2 
3 
3 
3 
-3 



Vi 






-1 

1 

2 
2 
3 
3 
3 
3 

-3 
3 
3 
3 
2 
2 
1 
-1 



























ARGUMENT XXXIV. 



Aig. 



o 


10 

20 

30 

40 

50 

60 

70 

80 

90 

100 
110 
120 
130 
140 
150 
160 
170 
180 



+3 
3 
3 
2 
2 
2 
1 

+1 




-1 
1 
2 
2 
3 
3 
3 
3 

-3 



Vi 




+1 
1 
2 
2 
2 
3 
3 
3 
3 

+3 
3 
2 
2 
2 
1 

+1 



















































180^ are to be sabtracted from the Aigaments > 180^, and li, 171, and ti to be taken with the reyeraed sign. 



77 



• 

• 

TABLE lY .—rCcyniimied. 




% 


PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. 


ARGUMENT XXXV. 


ARGUMENT XXXVI. 

* 


ARGUMENT XXXVII. 


An?. 


h 


^\ 


Ci 


AiK. 


6 


Vi 


Ci 


Arg. 


& 


^1 


& 


o 



-3 


+1 





o 




-2 








o 



+2 


+ 2 


-1 


10 


3 







10 


2 








10 


2 


4 





20 


3 







20 


2 


-1 





20 


2 


6 





30 


2 







30 


2 


1 





30 


2 


7 





40 


2 







40 


2 


1 





40 


2 


9 





50 


2 


+1 





50 


1 


2 





50 


2 


. 10 





60 


2 








60 


1 


2 





60 


2 


11 





70 


1 








70 


-1 


2 





70 


1 


11 


+1 


80 


-1 








80 





2 





80 


1 


12 




90 











90 





2 





90 


+1 


11 




100 











100 


+1 


-2 





100 





+11 


+1 


110 


+1 


— X 





110 


1 


2 





110 





10 




120 


1 







120 


1 


2 





120 


-1 


9 




130 


1 







130 


^ 


2 





130 


1 


7 




140 


2 







140 


2 


1 





140 


1 


6 




150 


2 







150 


2 


1 





150 


2 


4 




160 


2 







160 


2 


-1 





160 


2 


+ 2 




170 


2 


• 1 





170 


2 








170 


2 





J. 


180 


+3 


—1 





180 


+2 








180 


-2 


- 2 


+1 


ARGUMENT XXXVIH. 


ARGUMENT XXXIX. 


ARGUMENT XL. 


Arg. 


h 


^1 


& 


Arg. 


?i 


ni 


Ix 


Arg. 


& 


^\ 


cl 


o 



-2 


+4 





o 



-2 


-2 


+2 


o 



-2 








20 


3 


4 





20 


2 


-1 


1 


20 


2 


-1 


• 


40 


4 


3 





40 


3 





1 


40 


1 


1 





60 


4 


2 





60 


3 


+1 


+1 


60 


-1 


2 





80 


3 


+1 





80 


2 


1 





80 





2 





100 


3 


-1 


+1 


100 


2 


2 





100 


+1 


2 





120 


-2 


2 


1 


120 


-1 


3 


-1 


120 


1 


1 





140 





3 


+1 


140 





3 


1 


140 


2 


-1 





160 


+1 


4 





160 


+1 


3 


1 


160 


2 








180 • 


+2 


-4 





180 


+2 


+2 


-2 


ISO 


+2 








180° are to be subtracted from the Arguments > 180°, and ^, m» and Ci tG 


) be taken with the reyerscd sign. 





I 






•'T^i.^ 



m^f^ 



78 



TABLE lY.— Concluded. 

PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. 



ARGU^fENT XLI. 



Arg. 





20 

40 

60 

80 

100 

120 

140 

160 

180 



& 


Vi 


-1 





1 


+1 


-1 














a 




+1 




1 


+1 


1 





+1 






^1 

















ARGUMENT XLII. 



Arg. 





20 

40 

60 

80 

100 

120 

140 

160 

180 



ft 



m 



-1 




+1 
1 

2 
2 
2 
1 

+1 



+2 
2 
2 
2 
1 

+1 


-1 
1 

-2 
















ARGUMENT XLm. 



Aig. 



o 



20 

40 

60 

80 

100 

120 

140 

160 

180 



-1 

1 

-1 





+1 
1 
1 

+1 



Vl 

























ARGUMENT XLIV. 



Arg. 



& 





20 

40 

60 

80 

100 

120 

149 

160 

183 



-1 
1 
1 

-1 






+1 

+1 



m 



+1 








-1 

1 

-1 
















ARGUMENT XLV. 



Arg. 



o 


20 

40 

60 

80 

100 

120 

140 

160 

180 



ft 












Vi 






, -1 
1 

2 
2 
2 

1 

-1 


















180° are to be sobtracted from the Arguments > 180°, and ^i, m, and ti to be taken with the leyersed sigOb 



79 











TABLE V 


• 








LOGARITHMS FOR REFERRING THE PERTURBATIONS TO THE EQUATOR. | 








Mean Eqainox of tho beginning 


of the Tear. 








Tean. 


cos {xi x) 


COS (yiar) 


cos {zi x) 


cos (zi y) 


cos {tfiy) 


cos (ziy) 


cos {xi g) 


cos (yi«) 


cos («i«) 


1852 B 


9.982316 


9.423945n 


8.944771 


9.446013 


9.966907 


9.400926n 


8.16976571 


9.425327 


9.983980 


1853 


9.982289 


9.424326n 


8.944586 


9.446346 


9.966860 


9.400692» 


6.16702271 


9.425285 


9.963984 


1854 


9.982261 


9.424707n 


8.944400 


9.446679 


9.966852 


9.400658n 


8.16426571 


9.425243 


9.983988 


1855 


9.982234 


9.425088n 


8.944215 


9.447012 


9.966824 


9.400624n 


8.16148871 


9.425201 


9.963992 


1856 B 


9.982206 


9.425468n 


8.944029 


9.447345 


9.966796 


9.400791» 


8.15867471 


9.425159 


9.983996 


1857 


9.982179 


9.425648n 


8.943844 


9.447677 


9.966768 


9.400757» 


8.15583271 


9.425117 


9.984000 


1858 


9.982151 


9.426227» 


8.943658 


9.448009 


9.966740 


9.400723n 


8.15299171 


9.425075 


9.984004 


1^9 


9.982123 


9.426606» 


8.943472 


9.448341 


9.966712 


9.400689n 


8.15014271 


9.425033 


9.984008 


1860 B 


9.982095 


9.426984n 


8.943286 


9.448673 


9.966684 


9.400656n 


8.14726371 


9.424990 


9.984011 


1861 


^.982068 


9.427362n 


8.943100 


9.449004 


9.966656 


9.400622n 


8.144356n 


9.424948 


9.984015 


1668 


9.982040 


9.427740n 


8.942914 


9.449335 


9.966628 


9.400588» 


8.14141871 


9.424905 


9.984019 


1863 


9.982012 


9.428117n 


8.942728 


9.440666 


9.966600 


9400554n 


8.13647271 


9.424863 


9.984023 


1864 B 


9.981984 


9.428494n 


8.942541 


9.449906 


9.966572 


9.400521 n 


8.13551471 


9.424820 


9.964027 


1865 


9.981956 


9.428871n 


8.942355 


9.450326 


9.966544 


9.4004679 


6.13254871 


9.424778 


9.964031 


1866 


9.981928 


9.429247n 


8.942168 


9.450656 


9.966516 


9.400454» 


6.12954971 


9.424735 


9.984035 


1867 


9.981900 


9.429623n 


8.941981 


9.450986 


9.966488 


9.400420n 


8.12652171 


9.424693 


9.984039 


1868 B 


9.981872 


9.429999n 


8.941794 


9.451315 


9.966459 


9.400387n 


8.12346671 


9.424650 


9.984042 


1869 


9.981644 


9.430374n 


8.941607 


9.451644 


9.966431 


9.400353n 


6.12040971 


9.424606 


9.984046 


1870 


9.981816 


9.43074971 


8.941420 


9.451972 


9.966403 


9.40032Cn 


6.11733871 


9.424565 


9.964050 


1871 


9.981788 


9.431 124n 


8.941233 


9.452301 


9.966375 


9.400286n 


8.11424471 


9.424522 


9.984054 


1872 B 


9.981760 


9.431496n 


8.941045 


9.452629 


9.966346 


9.400253n 


8.11111471 


9.424479 


9.984058 


1873 


9.981732 


9.431872n 


8.940858 


9.452057 


9.966318 


9.40021971 


6.10795671 


9.424437 


9.984G62 


1874 


9.981704 


9.432245n 


8.940670 


9.45.'J284 


9.966290 


9.400186n 


8.10479471 


9.424394 


9.964C66 


1875 


9.981676 


9.432618n 


8.940483 


9.453612 


9.966262 


9.40015271 


8.10161071 


9.424351 


9.984070 


1876 B 


9.981647 


9.432991n 


8.94C295 


9.453939 


9.966233 


9.40011971 


8.09836771 


9.424308 


9.984073 


1877 


9.981619 


9.433364n 


8.940107 


9.454266 


9.966205 


9.40008571 


6.09513471 


9.424265 


9.964077 


1878 


9.981591 


9.433736n 


8.939919 


9.454592 


9.966177 


9.400062n 


8.09187871 


9.424222 


9.964C81 


1879 


9.981563 


9.434108n 


8.939731 


9.454918 


9.966149 


9.400019n 


8.08859771 


9.424179 


9.984085 


1880 B 


9.981534 


9.434479n 


8.939543 


9.455244 


9.966120 


9.399966n 


8.08527571 


9.424136 


9.984086 


1881 


9.981506 


9.434850n 


8.939355 


9.455570 


9.966092 


9.39995271 


8.08192371 


9.424093 


9.984092 


1882 


9.981478 


9.43522in 


8.939167 


9.455895 


9.966063 


9.39991971 


8.078529n 


9.424050 


9.9840C6 


1883 


9.981450 


9.435591» 


8.938979 


9.456220 


9.966035 


9.39968671 


6.07511971 


9.424007 


9.964100 


1884 B 


9.981421 


9.43596in 


8.938790 


9.456545 


9.966006 


9.39985371 


8.07171171 


9.423964 


9.984103 


1885 


9.961393 


9.436331» 


8.936632 


9.456869 


9.965978 


9.39961 9n 


8.C6826571 


9.423921 


9.984107 


1886 


9.981364 


9.436700» 


8.936413 


9.457193 


9.965949 


9.399786» 


8.06479571 


9.423878 


9.984111 


1887 


9.981336 


9.437069n 


8.938224 


9.457517 


9.965921 


9.399753n 


8.C613C271 


9.423835 


9.984115 


1888 B 


9.981307 


9.437438n 


8.938035 


9.457841 


9.965892 


9.399720n 


8.05776271 


9.423791 


9.984119 


1889 


9.981279 


9.437807» 


6.937846 


9.458164 


9.965864 


9.399687» 


8.05419271 


9.423746 


9.984123 


1890 


9.981250 


9.4381 75n 


8.937657 


9.458487 


9.965835 


9.39965471 


8.05061271 


9.423704 


9.984127 


1891 


9.981222 


9.438543n 


8.937466 


9.458810 


9.965806 


9.39962171 


8.04698271 


9.423661 


9.984131 


1892 B 


9.981193 


9.438910n 


8.937278 


9.459133 


9.965777 


9.399588» 


8.04332371 


9.423617 


9.964134 


1893 


9.981165 


9.439277n 


8.937089 


9.459455 


9.965749 


9.399555» 


8.03965271 


9.423573 


9.964136 


1894 


9.981136 


9.439644n 


8.936899 


9.459777 


9.965720 


9.399522n 


8.0a'>95n7i 


9.423529 


9.984142 


1895 


9.981108 


9.44001 In 


8.936709 


9.469099 


9.965691 


9.399489n 


8.03221671 


9.423485 


9.984146 


1896 B 


9.961079 


9.440377n 


8.936519 


9.460420 


9.965662 


9.399456n 


6.02844971 


9.423442 


9.984149 


1897 


9.961051 


9.440743n 


8.936329 


9.460741 


9.965634 


9.39942371 


8.02465071 


9.423396 


9.984153 


1898 


9.981022 


9.44110871 


8.936139 


9.461061 


9.965605 


9.39939071 


8.020817m 


9.423355 


9.984157 


1899 


9.980993 


9.441474n 


8.935949 


9.461382 


9.965576 


9.39935771 


8.01695071 


9.423311 


9.984161 


1900 B 


9.980964 


9.441839n 


8.9a5758 


9.461702 


9.965547 


9.39932571 


6.01304871 


9.423268 


9.964164 



80 







TABLE VI 


* 










CONSTANTS FOR THE EQUATOR. 








n 
d 


EqnAtor and mean Eqoinox at the beginning of the Year. 






Tean. 


A' 


B' 


C 


log sin a. 


log Bin 6. 


log sin c. 


1852 B 


1 u 

105 27 14.0 


O 1 u 

16 46 17.2 


O 1 N 

356 49 20.7 


9.998310 


9.986785 


9.425995 


1853 


105 28 3.8 


16 47 4.6 


366 50 31.7 


9.998311 


9.985787 


9.425945 


1854 


105 28 53.6 


16 47 52.0 


356 51 42.7 


9.998313 


9.985790 


9.426896 


1855 


105 29 43.5 


16 48 39.2 


356 52 53.8 


9.998314 


9.985792 


9.426844 


1856 B 


105 30 33.4 


16 49 26.8 


356 54 5.0 


9.996316 


9.965794 


9.425794 


1857 


105 31 23.2 


16 50 14.2 


356 55 16.1 


9.998317 


9.985797 


9.425744 


1858 


105 32 13.0 


16 51 1.6 


356 56 27.1 


9.998319 


9.985799 


9.425694 


1859 


105 33 2.9 


16 51 49.0 


356 57 38.2 


9.998320 


9.985801 


9.425644 


1860 B 


105 33 52.8 


16 52 36.5 


356 58 49.5 


9.998321 


9.985804 


9.425603 


1961 


105 34 42.6 


16 53 23.8 


357 0.6 


9.998323 


9.9858C6 


9.426643 


1862 


105 35 32.4 


16 54 11.2 


357 1 11.7 


9.996324 


9.985808 


9.426493 


1863 


105 % 22.2 


16 54 58.6 


357 2 22.9 


9.998326 


9.98681 1 


9.425443 


1864 B 


105 37 12.2 


16 55 46.1 


357 3 34.2 


9.996327 

• 


9.985613 


9.425392 


1865 


105 38 2.0 


1& 56 33.5 


357 4 45.4 


9.998329 


9.985815 


9.425342 


1866 


105 38 51.8 


16 57 20.9 


357 5 56.5 


9.996330 


9.986818 


9.425292 


1867 


105 39 41.6 


16 58 8J2 


357 7 7.7 


9.998331 


9.986820 


9.425242 


1868 B 


105 40 31.6 


16 58 55.8 


357 8 19.1 


9.998333 


9.985822 


9.425192 


1869 


105 41 21.4 


16 59 43.1 


357 9 30.3 


9.998334 


9.965825 


9.425142 


1870 


105 42 11.2 


17 30.5 


357 10 41.5 


9.998336 


9.966827 


9.425092 


1871 


105 43 1.0 


17 1 17.9 


357 11 52.7 


9.998337 


9.965829 


9.425042 


1872 B 


105 43 50.9 


17 2 5.4 


357 13 4.1 


9.998339 


9.965831 


9.424991 


1873 


105 44 40.7 


17 2 52.8 


357 14 15.4 


9.996340 


9.985634 


9.424941 


1874 


105 45 30.5 


17 3 40.2 


357 15 26.6 


9.998342 


9.966836 


9.424891 


1875 


105 46 20.3 


17 4 27.6 


357 16 37.9 


9.998343 


9.985838 


9.424841 


1876 B 


105 47 10.3 


17 5 15.1 


357 17 49.3 


9.998344 


9.965840 


9.424791 


1877 


105 48 0.1 


17 6 2.5 


357 19 0.6 


9.998346 


9.986843 


9.424741 


1878 


105 48 49.9 


17 6 49.8 


357 20 11.9 


9.996347 


9.985846 


9.424691 


1879 


105 49 39.7 


17 7 37.2 


357 21 23.2 


9.998349 


9.986847 


9.424641 


1880 B 


105 50 29.7 


17 8 24.7 


357 22 34.7 


9.998350 


9.985849 


9.424691 


1881 


105 51 19.5 


17 9 12.1 


357 23 46.0 


9.998352 


9.985652 


9.424641 


1882 


105 52 9.3 


17 9 59.5 


357 24 57.3 


9.998353 


9.986854 


9.424491 


1883 


105 52 59.1 


17 10 46.9 


357 26 8.7 


9.998354 


9.985856 


9.424441 


1884 B 


105 53 49.0 


yr 11 34.4 


357 27 20.2 


9.998356 


9.986858 


9.424391 


1885 


105 54 38.8 


17 12 21.8 


357 28 31.6 


9.998357 


9.985860 


9.424341 


1886 


105 55 28.6 


17 13 9.1 


357 29 42.9 


9.998369 


9.986863 


9.424291 


1887 


105 56 18.4 


17 13 56.5 


357 30 54.3 


9.998360 


9.986865 


9.424241 


1888 B 


105 57 8.4 


17 14 44.0 


357 32 5.9 


9.998361 


9.965867 


9.424191 


1889 


105 57 58.2 


17 15 31.4 


357 33 17.3 


9.998363 


9.986869 


9.424141 


1890 


105 58 48.0 


17 16 18.8 


357 34 28.7 


9.996364 


9.985871 


9.424091 


1891 


105 59 37.8 


17 17 6.2 


357 35 40.2 


9.998366 


9.985874 


9.424041 


1892B 


106 27.7 


17 17 53.7 


357 36 51.8 


9.998367 


9.985876 


9.423991 


1893 


106 1 17.5 


17 18 41.1 


357 38 3.2 


9.996369 


9.985878 


9.423941 


1894 


106 2 7.3 


17 19 28.5 


357 39 14.7 


9.998370 


9.985880 


9.423891 


1895 


106 2 57.2 


17 20 15.9 


357 40 26.2 


9.998371 


9.986882 


9.423841 


1896 B 


106 3 47.1 


17 21 3.4 


357 41 37.8 


9.998373 


9.965884 


9.423792 


1807 


106 4 36.9 


17 21 50.8 


357 42 49.4 


9.998374 


9.985886 


9.423742 


1898 


106 5 26.7 


17 22 38.1 

• 


357 44 0.9 


9.998376 


9.986888 


9.423692 


1899 


106 6 16.5 
106 7 6.5 


17 23 25.5 


357 45 12.4 


9.998377 


9.985890 


9.423642 


1900 B 


17 24 13.0 


357 46 24.1 


9.998379 


9.985893 


9.423592 






\ 



A 



•:>^'-ia